Class 10th Science CBSE Solution
In Text Questions-pg-200- What does an electric circuit mean?
- Define the unit of current.
- Calculate the number of electrons constituting one coulomb of charge.…
In Text Questions-pg-202- Name a device that helps to maintain a potential difference across a conductor.…
- What is meant by saying that the potential difference between two points is 1 V?…
- How much energy is given to each coulomb of charge passing through a 6 V battery?…
In Text Questions-pg-209- On what factors does the resistance of a conductor depend?
- Will current flow more easily through a thick wire or a thin wire of the same material,…
- Let the resistance of an electrical component remain constant while the potential…
- Why are coils of electric toasters and electric irons made of an alloy rather than a pure…
- Use the data in Table on page 23 of this book to answer the following: (a) Which among…
In Text Questions-pg-213- Draw a schematic diagram of a circuit consisting of a battery of three cells of 2 V each,…
- Redraw the circuit of Question 1 putting an ammeter to measure the current through the…
In Text Questions-pg-216- Judge the equivalent resistance when the following are connected in parallel: (a) 1 and…
- An electric lamp of 100, a toaster of resistance 50 , and a water filter of resistance 500…
- What are the advantages of connecting electrical devices in parallel with the battery…
- How can three resistors of resistances 2, 3, and 6 be connected to give a total resistance…
- What is (a) the highest, and (b) the lowest, total resistance that can be secured by the…
In Text Questions-pg-218- What determines the rate at which energy is delivered by a current?…
- Why does the cord of an electric heater not glow while the heating element does?…
- Compute the heat generated while transferring 96000 coulombs of charge in one hour through…
- An electric motor takes 5A from a 220 V line. Determine the power of the motor and the…
- An electric iron of resistance20 takes a current of 5 A. Calculate the heat developed in…
Exercise-pg-221- A piece of wire of resistance R is cut into five equal parts. These parts are then…
- Which of the following terms does not represent electrical power in a circuit?A. I^2 R B.…
- An electric bulb is rated 220 V and 100 W. When it is operated on 110 V, the power…
- Two conducting wires of the same material and of equal lengths and equal diameters are…
- How is a voltmeter connected in the circuit to measure the potential difference between…
- A copper wire has diameter 0.5 mm and resistivity of 1.6 x 10-8 m. What will be the length…
- The values of current I flowing in a given resistor for the corresponding values of…
- When a 12 V battery is connected across an unknown resistor, there is a current of 2.5 mA…
- A battery of 9 V is connected in series with resistors of 0.2, 0.3, 0.4 , 0.5 and 12…
- How many 176 resistors in parallel are required to carry 5 A on a 220 V line?…
- Show how you would connect three resistors, each of resistance 6, so that the combination…
- Several electric bulbs designed to be used on a 220 V electric supply line are rated 10 W…
- A hot plate of an electric oven connected to a 220 V line has two resistance coils A and…
- Compare the power used in the 2resistor in each of the following circuits: (i) a 6 V…
- Two lamps, one rated 100 W at 220 V and the other 60 W at 220 V are connected in parallel…
- Which uses more energy, a 250 W TV set in 1hr or a 1200 W toaster in 10 minutes ?…
- An electric heater of resistance 8draws 15 A from the service mains for 2 hours. Calculate…
- Explain the following: (a) Why is the tungsten used almost exclusively for the filament of…
- What does an electric circuit mean?
- Define the unit of current.
- Calculate the number of electrons constituting one coulomb of charge.…
- Name a device that helps to maintain a potential difference across a conductor.…
- What is meant by saying that the potential difference between two points is 1 V?…
- How much energy is given to each coulomb of charge passing through a 6 V battery?…
- On what factors does the resistance of a conductor depend?
- Will current flow more easily through a thick wire or a thin wire of the same material,…
- Let the resistance of an electrical component remain constant while the potential…
- Why are coils of electric toasters and electric irons made of an alloy rather than a pure…
- Use the data in Table on page 23 of this book to answer the following: (a) Which among…
- Draw a schematic diagram of a circuit consisting of a battery of three cells of 2 V each,…
- Redraw the circuit of Question 1 putting an ammeter to measure the current through the…
- Judge the equivalent resistance when the following are connected in parallel: (a) 1 and…
- An electric lamp of 100, a toaster of resistance 50 , and a water filter of resistance 500…
- What are the advantages of connecting electrical devices in parallel with the battery…
- How can three resistors of resistances 2, 3, and 6 be connected to give a total resistance…
- What is (a) the highest, and (b) the lowest, total resistance that can be secured by the…
- What determines the rate at which energy is delivered by a current?…
- Why does the cord of an electric heater not glow while the heating element does?…
- Compute the heat generated while transferring 96000 coulombs of charge in one hour through…
- An electric motor takes 5A from a 220 V line. Determine the power of the motor and the…
- An electric iron of resistance20 takes a current of 5 A. Calculate the heat developed in…
- A piece of wire of resistance R is cut into five equal parts. These parts are then…
- Which of the following terms does not represent electrical power in a circuit?A. I^2 R B.…
- An electric bulb is rated 220 V and 100 W. When it is operated on 110 V, the power…
- Two conducting wires of the same material and of equal lengths and equal diameters are…
- How is a voltmeter connected in the circuit to measure the potential difference between…
- A copper wire has diameter 0.5 mm and resistivity of 1.6 x 10-8 m. What will be the length…
- The values of current I flowing in a given resistor for the corresponding values of…
- When a 12 V battery is connected across an unknown resistor, there is a current of 2.5 mA…
- A battery of 9 V is connected in series with resistors of 0.2, 0.3, 0.4 , 0.5 and 12…
- How many 176 resistors in parallel are required to carry 5 A on a 220 V line?…
- Show how you would connect three resistors, each of resistance 6, so that the combination…
- Several electric bulbs designed to be used on a 220 V electric supply line are rated 10 W…
- A hot plate of an electric oven connected to a 220 V line has two resistance coils A and…
- Compare the power used in the 2resistor in each of the following circuits: (i) a 6 V…
- Two lamps, one rated 100 W at 220 V and the other 60 W at 220 V are connected in parallel…
- Which uses more energy, a 250 W TV set in 1hr or a 1200 W toaster in 10 minutes ?…
- An electric heater of resistance 8draws 15 A from the service mains for 2 hours. Calculate…
- Explain the following: (a) Why is the tungsten used almost exclusively for the filament of…
In Text Questions-pg-200
Question 1.What does an electric circuit mean?
Answer:The electric circuit is the continuous path which allows electric current or electrons to flow through it. An electric circuit consists of connecting wires, other elements (like electric bulb, resistances, key etc.) and a battery.
Question 2.Define the unit of current.
Answer:The SI unit of electric current is Ampere, commonly denoted by letter A. 1 Ampere is defined as - When an amount of charge equivalent to 1 coulomb flows through a cross-section of a conductor in 1 second.
Question 3.Calculate the number of electrons constituting one coulomb of charge.
Answer:We know that, the charge of an electron, e = 1.6 X 10-19 Coulomb
Therefore, 1.6 X 10-19 C of charge is equivalent to = 1 electron
By unitary method,
If the charge is 1C then no of electrons
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)
Thus, 6.25
electrons constitute 1 coulomb of charge.
What does an electric circuit mean?
Answer:
The electric circuit is the continuous path which allows electric current or electrons to flow through it. An electric circuit consists of connecting wires, other elements (like electric bulb, resistances, key etc.) and a battery.
Question 2.
Define the unit of current.
Answer:
The SI unit of electric current is Ampere, commonly denoted by letter A. 1 Ampere is defined as - When an amount of charge equivalent to 1 coulomb flows through a cross-section of a conductor in 1 second.
Question 3.
Calculate the number of electrons constituting one coulomb of charge.
Answer:
We know that, the charge of an electron, e = 1.6 X 10-19 Coulomb
Therefore, 1.6 X 10-19 C of charge is equivalent to = 1 electron
By unitary method,
If the charge is 1C then no of electrons
In Text Questions-pg-202
Question 1.Name a device that helps to maintain a potential difference across a conductor.
Answer:An electric cell or a battery helps to maintain a potential difference across a conductor.
Question 2.What is meant by saying that the potential difference between two points is 1 V?
Answer:The potential difference between two points is said to be 1 volt (1V) if the amount of work done in moving a charge of 1 Coulomb (1C) between the two points is equivalent to 1 Joule (1J)
Question 3.How much energy is given to each coulomb of charge passing through a 6 V battery?
Answer:The charge passing through the battery is 1 coulomb. The potential difference is 6V. We have to find out the energy which is equal to the work done in moving the charge through 6V. Now,
![](data:image/png;base64,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)
Since the work done on each coulomb of charge is 6 joules. Therefore, the energy given to each coulomb of charge is also 6 joules.
Name a device that helps to maintain a potential difference across a conductor.
Answer:
An electric cell or a battery helps to maintain a potential difference across a conductor.
Question 2.
What is meant by saying that the potential difference between two points is 1 V?
Answer:
The potential difference between two points is said to be 1 volt (1V) if the amount of work done in moving a charge of 1 Coulomb (1C) between the two points is equivalent to 1 Joule (1J)
Question 3.
How much energy is given to each coulomb of charge passing through a 6 V battery?
Answer:
The charge passing through the battery is 1 coulomb. The potential difference is 6V. We have to find out the energy which is equal to the work done in moving the charge through 6V. Now,
Since the work done on each coulomb of charge is 6 joules. Therefore, the energy given to each coulomb of charge is also 6 joules.
In Text Questions-pg-209
Question 1.On what factors does the resistance of a conductor depend?
Answer:The electrical resistance of a conductor depends on the factors listed below:
1) Nature of the material of the conductor – eg. A wire made of copper would be a better conductor than a wire made of iron
2) Length of the conductor – eg. A shorter wire would be a better conductor than a longer wire
3) Area of cross-section of the conductor – eg. A thick copper wire is a better conductor than a thin copper wire
4) Temperature of the conductor – resistance goes up with increase in temperature
Question 2.Will current flow more easily through a thick wire or a thin wire of the same material, when connected to the same source? Why?
Answer:The current will flow more easily through a thick wire than a thin wire of the same material when connected to the same source. This is mainly because the resistance of a wire is inversely proportional to the square of its diameter. And, a thick wire has greater diameter than a thin wire. Therefore, thick wire will offer less resistance to the current flow and thin wire will offer more resistance to the current flow. Thus, current flows easily through thick wire.
Question 3.Let the resistance of an electrical component remain constant while the potential difference across the two ends of the component decreases to half of its former value. What change will occur in the current through it?
Answer:We know, From Ohm’s Law: ![](data:image/png;base64,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)
Since the resistance is constant and the potential difference is decreased to half of the former value. Thus, the current through the component will also decrease to half of its former value.
Question 4.Why are coils of electric toasters and electric irons made of an alloy rather than a pure metal ?
Answer:The coils (or heating elements) of toasters and electric irons are made of an alloy rather than a pure metal due to the following two reasons:
1) The resistivity of an alloy is much higher than that of a pure metal, and
2) An alloy does not undergo oxidation easily even at high temperature
Question 5.Use the data in Table on page 23 of this book to answer the following:
(a) Which among iron and mercury is a better conduction?
(b) Which material is the best conductor?
Answer:(a) The electrical resistivity of iron is
. And, the electrical resistivity of mercury is
. Since the resistivity of mercury is greater than that of iron, it will offer more hindrance to current flow as compared to iron. Therefore, iron is a better conductor than mercury.
(b) Silver metal has the lowest resistivity nearly about 1.60 x 10-8
m. Therefore, silver metal is the best conductor of electricity.
On what factors does the resistance of a conductor depend?
Answer:
The electrical resistance of a conductor depends on the factors listed below:
1) Nature of the material of the conductor – eg. A wire made of copper would be a better conductor than a wire made of iron
2) Length of the conductor – eg. A shorter wire would be a better conductor than a longer wire
3) Area of cross-section of the conductor – eg. A thick copper wire is a better conductor than a thin copper wire
4) Temperature of the conductor – resistance goes up with increase in temperature
Question 2.
Will current flow more easily through a thick wire or a thin wire of the same material, when connected to the same source? Why?
Answer:
The current will flow more easily through a thick wire than a thin wire of the same material when connected to the same source. This is mainly because the resistance of a wire is inversely proportional to the square of its diameter. And, a thick wire has greater diameter than a thin wire. Therefore, thick wire will offer less resistance to the current flow and thin wire will offer more resistance to the current flow. Thus, current flows easily through thick wire.
Question 3.
Let the resistance of an electrical component remain constant while the potential difference across the two ends of the component decreases to half of its former value. What change will occur in the current through it?
Answer:
We know, From Ohm’s Law:
Since the resistance is constant and the potential difference is decreased to half of the former value. Thus, the current through the component will also decrease to half of its former value.
Question 4.
Why are coils of electric toasters and electric irons made of an alloy rather than a pure metal ?
Answer:
The coils (or heating elements) of toasters and electric irons are made of an alloy rather than a pure metal due to the following two reasons:
1) The resistivity of an alloy is much higher than that of a pure metal, and
2) An alloy does not undergo oxidation easily even at high temperature
Question 5.
Use the data in Table on page 23 of this book to answer the following:
(a) Which among iron and mercury is a better conduction?
(b) Which material is the best conductor?
Answer:
(a) The electrical resistivity of iron is . And, the electrical resistivity of mercury is
. Since the resistivity of mercury is greater than that of iron, it will offer more hindrance to current flow as compared to iron. Therefore, iron is a better conductor than mercury.
(b) Silver metal has the lowest resistivity nearly about 1.60 x 10-8m. Therefore, silver metal is the best conductor of electricity.
In Text Questions-pg-213
Question 1.Draw a schematic diagram of a circuit consisting of a battery of three cells of 2 V each, a 5
resistor, an 8
resistor, and a 12
resistor, and a plug key, all connected in series.
Answer:In this problem, we have 3 cells of voltage2 V each. Thus, the total voltage of the three cells connected together to form a battery will be 3 X 2V = 6V. The circuit also consists 3 resistors of 5
, 8
, 12
respectively and a plug key, all connected in series as shown in the figure given below:
![](data:image/png;base64,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)
Question 2.Redraw the circuit of Question 1 putting an ammeter to measure the current through the resistors and a voltmeter to measure the potential difference across the 12 n resistor. What would be the reading in the ammeter and the voltmeter?
![](data:image/png;base64,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)
Answer:We redraw the circuit by including an ammeter circuit and a voltmeter across the 12
resistor, as shown in figure. Please note that the ammeter is always connected n series with the circuit but the voltmeter has been put in parallel with the 12
resistor
We will now calculate the current reading in the ammeter and potential difference reading in the voltmeter:
(i) Calculation of current flowing in the circuit. The three resistors of 5
, 8
and 12
are connected in series. So, net resistance in series is the sum of all the resistances.
Ans: Total resistance, ![](data:image/png;base64,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)
Potential difference, V = 6 V
And, Current, I = ?
We know,
![](data:image/png;base64,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)
Since the current in the circuit is 0.24 A, therefore, the ammeter will show reading of 0.24 A.
(ii) Calculation of potential difference across the 12
resistor. From (i) we have calculated that a current of 0.24 A flows in the circuit. Since, in series same current flows through the whole circuit. The same current of 0.24 A also flows through the 12
.
Now, for the 12
resistor:
Current, I = 0.24 A
Resistance, R = 12 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAATCAMAAABFjsb+AAAAAXNSR0ICQMB9xQAAAGxQTFRFgYGBAAAAiIhmZoiIZnd3f39dXX9/d3ddf25ISG5/e2pEgFszM1uAM1l/M0ZuM0ZsbEYdHUZsbEYdWjMAADNaHR1ISB0AAB1ISBwAABxIMwAAAAAzMwAAAAAzHQAAAAAdHQAAAAAdAAAAAAAAIUJbnQAAACN0Uk5TAAEMDA0ZGRoxMTJMTE1kZXNzdKGhqbu7vLzc3N3d6+vs7P6yYo8GAAAAhklEQVR42qWP2w6CMBBEpwURi6ilWMAbuPv//0h6MyU+GedpcjYzmQV+k/DakI6c+gyqhTSAhrhNaP94H7zZ3fgYmeE+uoanwhs5fq71khIpmlk5fjNcsuwQ+iDtVIaZZk4JSDuUW1SfhVDXAjCtEOoUS5j5WbmdzKwDexHRvYK07meNv7QCXG4JGhu5Es8AAAAASUVORK5CYII=)
And, Potential difference, V =?
We know that,
![](data:image/png;base64,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)
Thus, the potential difference across the 12
resistor is 2.88V. So, the voltmeter will show a reading of 2.88 V.
Draw a schematic diagram of a circuit consisting of a battery of three cells of 2 V each, a 5 resistor, an 8
resistor, and a 12
resistor, and a plug key, all connected in series.
Answer:
In this problem, we have 3 cells of voltage2 V each. Thus, the total voltage of the three cells connected together to form a battery will be 3 X 2V = 6V. The circuit also consists 3 resistors of 5 , 8
, 12
respectively and a plug key, all connected in series as shown in the figure given below:
Question 2.
Redraw the circuit of Question 1 putting an ammeter to measure the current through the resistors and a voltmeter to measure the potential difference across the 12 n resistor. What would be the reading in the ammeter and the voltmeter?
Answer:
We redraw the circuit by including an ammeter circuit and a voltmeter across the 12 resistor, as shown in figure. Please note that the ammeter is always connected n series with the circuit but the voltmeter has been put in parallel with the 12
resistor
We will now calculate the current reading in the ammeter and potential difference reading in the voltmeter:
(i) Calculation of current flowing in the circuit. The three resistors of 5 , 8
and 12
are connected in series. So, net resistance in series is the sum of all the resistances.
Ans: Total resistance,
Potential difference, V = 6 V
And, Current, I = ?
We know,
Since the current in the circuit is 0.24 A, therefore, the ammeter will show reading of 0.24 A.
(ii) Calculation of potential difference across the 12 resistor. From (i) we have calculated that a current of 0.24 A flows in the circuit. Since, in series same current flows through the whole circuit. The same current of 0.24 A also flows through the 12
.
Now, for the 12 resistor:
Current, I = 0.24 A
Resistance, R = 12
And, Potential difference, V =?
We know that,
Thus, the potential difference across the 12 resistor is 2.88V. So, the voltmeter will show a reading of 2.88 V.
In Text Questions-pg-216
Question 1.Judge the equivalent resistance when the following are connected in parallel:
(a) 1
and 106![](data:image/png;base64,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)
(b) 1
,103
and 106![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAATCAMAAABFjsb+AAAAAXNSR0ICQMB9xQAAAGxQTFRFgYGBAAAAiIhmZoiIZnd3f39dXX9/d3ddf25ISG5/e2pEgFszM1uAM1l/M0ZuM0ZsbEYdHUZsbEYdWjMAADNaHR1ISB0AAB1ISBwAABxIMwAAAAAzMwAAAAAzHQAAAAAdHQAAAAAdAAAAAAAAIUJbnQAAACN0Uk5TAAEMDA0ZGRoxMTJMTE1kZXNzdKGhqbu7vLzc3N3d6+vs7P6yYo8GAAAAhklEQVR42qWP2w6CMBBEpwURi6ilWMAbuPv//0h6MyU+GedpcjYzmQV+k/DakI6c+gyqhTSAhrhNaP94H7zZ3fgYmeE+uoanwhs5fq71khIpmlk5fjNcsuwQ+iDtVIaZZk4JSDuUW1SfhVDXAjCtEOoUS5j5WbmdzKwDexHRvYK07meNv7QCXG4JGhu5Es8AAAAASUVORK5CYII=)
Answer:(a) The equivalent resistance of two resistances 1
and 106
connected in parallel will be less than 1
.This is because when a number of resistances are connected in parallel, then their equivalent resistance is less than the smallest individual resistance. Here, since the smallest resistance is 1
. Therefore, the net resistance will be less than 1![](data:image/png;base64,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)
(b) The equivalent resistance of three resistances1
,103
and 106
connected in parallel will be less than 1
because the smallest resistance is 1
.
Question 2.An electric lamp of 100
, a toaster of resistance 50
, and a water filter of resistance 500
are connected in parallel to a 220 V source. What is the resistance of an electric iron connected to the same source that takes as much current as all three appliances, and what is the current through it?
Answer:The combined resistance R of three resistors (or electrical devices) R1 R2 and R3, connected in parallel is given by the formula:
![](data:image/png;base64,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)
Here, Resistance of electric lamp, R1 = 100![](data:image/png;base64,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)
Resistance of toaster, R2 = 50![](data:image/png;base64,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)
Resistance of water filter, R 3 = 500 ![](data:image/png;base64,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)
Putting these values of R1 R2 and R3 in the above formula, we get:
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Thus, the resistance of electric iron will also be 31.25
.
Now, Potential difference, V= 220 V
Current, I =?
![](data:image/png;base64,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)
Thus, the current passing through the electric iron is 7.04 amperes.
Question 3.What are the advantages of connecting electrical devices in parallel with the battery instead of connecting them in series?
Answer:The advantages of connecting electrical devices in parallel rather than series are as follows:
a) The voltage is same across all the elements in case of parallel circuits. Even if any one of the electrical devices stop working, it will not affect other electrical appliances and they will work normally. On the other hand, in series circuit, the current through all devices is same. If one electrical appliance stops, Then the whole circuit is broken and no current flows. As a result, all other appliances also stop working.
b) In case of parallel circuits, each electrical appliance works independently, i.e. it has its own switch. Each device can be turned on or turned off independently, without affecting other appliances. In series circuit, all the electrical appliances have only one switch due to which they cannot be turned on or turned off independently.
c) In parallel circuits, each electrical appliance gets the same voltage as that of the battery due to which all the appliances work properly. In series circuit, the appliances do not get the same voltage but get the same current. Each appliance has a different voltage.
d) Parallel circuits divide the current among electrical devices hence each device get necessary current to operate properly.
Question 4.How can three resistors of resistances 2
, 3
, and 6
be connected to give a total resistance of
(a) 4
, and (b) 1
?
Answer:(a) In order to obtain a total resistance of 4
from three resistors of 2
, 3
and 6
.
Firstly, connect the two resistors of 3
and 6
in parallel to get a total resistance of 2
which is less than the lowest individual resistance.
![](data:image/jpeg;base64,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)
![](data:image/png;base64,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)
Then the net R from parallel connection is connected in series with the remaining 2 Q resistor to get a total resistance of 4 Q. This is because in series combination:
R = R1+ R2
R = 2 + 2
R = 4![](data:image/png;base64,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)
The arrangement of three resistors of 2,3
and 6
which gives a total resistance of 4
can now be represented as follows :
![](data:image/png;base64,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)
Thus, we can obtain a total resistance of 4
by connecting parallel combination of 3
and 6
resistors in series with 2
resistor.
(b) In order to obtain a total resistance of 1
from three resistors of 2
, 3
and 6Q, all the three resistors should be connected in parallel. This is because in parallel combination:
![](data:image/png;base64,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)
![](data:image/jpeg;base64,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)
Question 5.What is (a) the highest, and (b) the lowest, total resistance that can be secured by the combination of four coils of resistances 4
, 8
, 12
and 24
?
Answer:(a) The highest resistance can be secured (or obtained) by connecting all the four coils in series. In this case:
R = R1 + R2 + R3 + R4
R = 4 + 8 + 12 + 24
R = 48![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAATCAYAAAByUDbMAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAE8SURBVDjL1ZRBbsIwEEWHrukBqJhDkLlCFVkqHKCJsqMsqsgLWimLLpzscgzKrmeAm5RcgHIFoHaaBCexI4FQJSJ9ZeHx88z4jyFJEriW4F9g8utJ3RnUOwumNoUuvsv/QWqv6QCOt7RBW6CP10cHAXZqIzI+19figJ4K6JGexaQJrIGiKHgggAwAfxgXI1PWQgQDGbMpgVaYR/CpgoD8RVejY5/GedyQrWdp2m/B0nTWZ0NY5yf68bgLJjgb/bUCd3oFzfSzZkBHqZkVdsrsCjAlznBuaqz1xpGtjD2rskNY5Y2NonubmT0HlqYbbwVWQHVqA6jWfYKFBG1LkO612g2RG76UY5OXguxLL0NZpzBrFUMunxphhfOPJ1EWCDFo+VATuuGbDbatzyJ9l7Cq/Pqs7vWRg9t7zy7RL47h4hM71IF9AAAAAElFTkSuQmCC)
Thus, the highest resistance which can be secured is 48 ohms.
(b) The lowest resistance can be secured by connecting all the four coils in parallel. In this case:
![](data:image/png;base64,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)
Thus, the lowest resistance which can be secured is 2![](data:image/png;base64,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)
Judge the equivalent resistance when the following are connected in parallel:
(a) 1 and 106
(b) 1,103
and 106
Answer:
(a) The equivalent resistance of two resistances 1and 106
connected in parallel will be less than 1
.This is because when a number of resistances are connected in parallel, then their equivalent resistance is less than the smallest individual resistance. Here, since the smallest resistance is 1
. Therefore, the net resistance will be less than 1
(b) The equivalent resistance of three resistances1,103
and 106
connected in parallel will be less than 1
because the smallest resistance is 1
.
Question 2.
An electric lamp of 100, a toaster of resistance 50
, and a water filter of resistance 500
are connected in parallel to a 220 V source. What is the resistance of an electric iron connected to the same source that takes as much current as all three appliances, and what is the current through it?
Answer:
The combined resistance R of three resistors (or electrical devices) R1 R2 and R3, connected in parallel is given by the formula:
Here, Resistance of electric lamp, R1 = 100
Resistance of toaster, R2 = 50
Resistance of water filter, R 3 = 500
Putting these values of R1 R2 and R3 in the above formula, we get:
Thus, the resistance of electric iron will also be 31.25.
Now, Potential difference, V= 220 V
Current, I =?
Thus, the current passing through the electric iron is 7.04 amperes.
Question 3.
What are the advantages of connecting electrical devices in parallel with the battery instead of connecting them in series?
Answer:
The advantages of connecting electrical devices in parallel rather than series are as follows:
a) The voltage is same across all the elements in case of parallel circuits. Even if any one of the electrical devices stop working, it will not affect other electrical appliances and they will work normally. On the other hand, in series circuit, the current through all devices is same. If one electrical appliance stops, Then the whole circuit is broken and no current flows. As a result, all other appliances also stop working.
b) In case of parallel circuits, each electrical appliance works independently, i.e. it has its own switch. Each device can be turned on or turned off independently, without affecting other appliances. In series circuit, all the electrical appliances have only one switch due to which they cannot be turned on or turned off independently.
c) In parallel circuits, each electrical appliance gets the same voltage as that of the battery due to which all the appliances work properly. In series circuit, the appliances do not get the same voltage but get the same current. Each appliance has a different voltage.
d) Parallel circuits divide the current among electrical devices hence each device get necessary current to operate properly.
Question 4.
How can three resistors of resistances 2, 3
, and 6
be connected to give a total resistance of
(a) 4, and (b) 1
?
Answer:
(a) In order to obtain a total resistance of 4 from three resistors of 2
, 3
and 6
.
Firstly, connect the two resistors of 3 and 6
in parallel to get a total resistance of 2
which is less than the lowest individual resistance.
R = R1+ R2
R = 2 + 2
R = 4
The arrangement of three resistors of 2,3 and 6
which gives a total resistance of 4
can now be represented as follows :
Thus, we can obtain a total resistance of 4by connecting parallel combination of 3
and 6
resistors in series with 2
resistor.
(b) In order to obtain a total resistance of 1 from three resistors of 2
, 3
and 6Q, all the three resistors should be connected in parallel. This is because in parallel combination:
Question 5.
What is (a) the highest, and (b) the lowest, total resistance that can be secured by the combination of four coils of resistances 4, 8
, 12
and 24
?
Answer:
(a) The highest resistance can be secured (or obtained) by connecting all the four coils in series. In this case:
R = R1 + R2 + R3 + R4
R = 4 + 8 + 12 + 24
R = 48
Thus, the highest resistance which can be secured is 48 ohms.
(b) The lowest resistance can be secured by connecting all the four coils in parallel. In this case:
Thus, the lowest resistance which can be secured is 2
In Text Questions-pg-218
Question 1.What determines the rate at which energy is delivered by a current?
Answer:Electric power of the appliance the rate at which energy is delivered by a current.
Question 2.Why does the cord of an electric heater not glow while the heating element does?
Answer:The heating element of an electric heater is made of an alloy example nichrome, which has high resistance whereas the cord is made of copper metal which has very low resistance as compared to the heating element. Now, the heating element of an electric heater made of nichrome glows because it becomes red-hot due to the large amount of heat produced on passing current. On the other hand, the connecting cord of the electric heater made of copper does not glow because negligible heat is produced in it by passing the same current (due to its extremely low resistance).
Question 3.Compute the heat generated while transferring 96000 coulombs of charge in one hour through a potential difference of 50 V.
Answer:First of all we will calculate the current (I) by using the given values of charge (Q) and time (t). We know that:
Current , I =
![](data:image/png;base64,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)
We will now calculate the resistance by using Ohm's law:
Resistance,
= 1.87![](data:image/png;base64,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)
And, Time, t= 1h = 60x60s = 3600 s
Heat generated, H= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= 4788397J
=
or ![](data:image/png;base64,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)
Thus, the heat generated is 4.8 x 106 joules.
Question 4.An electric motor takes 5A from a 220 V line. Determine the power of the motor and the energy consumed in 2 h.
Answer:Here,
Voltage, V = 220 V
Current, I = 5 A
Power, P = V x I = 220V X 5 A = 1100 Watts
Thus, the power of the motor is 1100 watts.
Now,
Power, P = 1100 W (Calculated above)
Time, t = 2 hour = 2 x 60 min x 60 sec
= ![](data:image/png;base64,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)
= 7200 s
So, Energy, E = P x t
E = 1100W X 7200 sec
= 7.92x
J
Thus, the energy consumed is 7.92 x 106 joules.
Question 5.An electric iron of resistance20
takes a current of 5 A. Calculate the heat developed in 30 s.
Answer:Here, Current, I = 5 A
Resistance, R = 20![](data:image/png;base64,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)
Time, t = 30 s
Now, we know, Heat produced is given as,
![](data:image/png;base64,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)
Thus, the heat developed is 15000 joules.
What determines the rate at which energy is delivered by a current?
Answer:
Electric power of the appliance the rate at which energy is delivered by a current.
Question 2.
Why does the cord of an electric heater not glow while the heating element does?
Answer:
The heating element of an electric heater is made of an alloy example nichrome, which has high resistance whereas the cord is made of copper metal which has very low resistance as compared to the heating element. Now, the heating element of an electric heater made of nichrome glows because it becomes red-hot due to the large amount of heat produced on passing current. On the other hand, the connecting cord of the electric heater made of copper does not glow because negligible heat is produced in it by passing the same current (due to its extremely low resistance).
Question 3.
Compute the heat generated while transferring 96000 coulombs of charge in one hour through a potential difference of 50 V.
Answer:
First of all we will calculate the current (I) by using the given values of charge (Q) and time (t). We know that:
Current , I =
We will now calculate the resistance by using Ohm's law:
Resistance, = 1.87
And, Time, t= 1h = 60x60s = 3600 s
Heat generated, H=
=
= 4788397J
= or
Thus, the heat generated is 4.8 x 106 joules.
Question 4.
An electric motor takes 5A from a 220 V line. Determine the power of the motor and the energy consumed in 2 h.
Answer:
Here,
Voltage, V = 220 V
Current, I = 5 A
Power, P = V x I = 220V X 5 A = 1100 Watts
Thus, the power of the motor is 1100 watts.
Now,
Power, P = 1100 W (Calculated above)
Time, t = 2 hour = 2 x 60 min x 60 sec
=
= 7200 s
So, Energy, E = P x t
E = 1100W X 7200 sec
= 7.92xJ
Thus, the energy consumed is 7.92 x 106 joules.
Question 5.
An electric iron of resistance20 takes a current of 5 A. Calculate the heat developed in 30 s.
Answer:
Here, Current, I = 5 A
Resistance, R = 20
Time, t = 30 s
Now, we know, Heat produced is given as,
Thus, the heat developed is 15000 joules.
Exercise-pg-221
Question 1.A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R', then the ratio R/R' is:
A. 1/25
B. 1/5
C. 5
D. 25
Answer:The resistance of wire is R. This wire is cut into five equal pieces as a result resistance of each piece of wire will be R⁄5.Now, when these five pieces are connected in parallel, the equivalent resistance for the combination is R’. We can write,
(Assume that each piece of wire is named R1, R2, R3, R4, R5)
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)
Thus, the correct answer is: Option (d)
Question 2.Which of the following terms does not represent electrical power in a circuit?
A. I2R
B. IR2
C. VI
D. V2/R
Answer:the electrical power is not represented as IR2
Question 3.An electric bulb is rated 220 V and 100 W. When it is operated on 110 V, the power consumed will be:
A. 100 W
B. 75 W
C. 50 W
D. 25 W
Answer:The bulb parameters are as given below:
Power, P = 100W
Potential difference, V = 220V
Then Resistance, R = ?
Now,
![](data:image/png;base64,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)
This resistance of the bulb will remain constant i.e. 484 ![](data:image/png;base64,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)
Now, when we operate this bulb on 110 V, then,
Power, P =?
Potential difference, V = 110V
And, resistance, R = 484![](data:image/png;base64,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)
P = ![](data:image/png;base64,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)
P =
=
= 25 W
Thus, the correct answer is: (d) 25 W.
Question 4.Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then in parallel in a circuit across the same potential difference. The ratio of heat produced in series and parallel combination would be:
A. 1 : 2
B. 2 : 1
C. 1 : 4
D. 4 : 1
Answer:Suppose the resistance of each one of the two wires is R.
Case (i) When both wires are connected in series. Then, net resistance will be R+
R = 2R.
According to Ohms Law:
Current(I)= ![](data:image/png;base64,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)
Then, heat produced will be
( As H = I2 X R X T)
Case (ii) When both wires are connected in parallel. Then, net resistance will be ![](data:image/png;base64,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)
According to Ohms Law:
Current(I)= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFAAAAAzCAYAAAAAcY9ZAAADRklEQVRoge2aPWgUQRiGn+YgxcE1IUVAQeGKhGAjXECEWARCUEkRCBZpLE44IdEiYKmFEOFEAoqCECFgQCV4ENAi+AORICKCsVJUsEgKi1ikSGNxFt+suZ/Znd3buds9bh6Y4nY+5t57b3fmm9kPHI60UgBmNe1MhPjhtqtMMQXgIvANqAJfgCJwKiB+RcV+AErAkfbL/M8l4AXwBvgBrOGvtaPcQUy5FSJ2HHgOZNqqqJkV5M/2yALPEN1XOqyliXkl5LEhLgNUgFzbFdVzHljQXO9D7sQqCd+JZ5WITUPcHDATcswCcCyiBr+7ugJ8BiY1fWVE+6MI32WdESViJyBmEHgaYczrwC6QDxFbVrFZn/4Npa+i6Suqvo0I2qyTUyKq+P+IVaIvGJ4xQSaGiZlE5sBRTd9N/M3tKL+VkCFN3zRwtcVxgwwKY56JV4juyzHGsMJ7JWSi4XoO+XfjrLo6o2yYdwLR/InOZwVNPEHElBqu30YWhLjUGmbDvAywpcYZjK3OAt5qVq65VkAMtPkdB8Q3D2AR+GlhHGuUEAPX1OcMsI7dnK8M/CW+gUVgGxiwIcoWE4iBH9XnBWTxsIX32A4jO4hWTZxGtnKN2UJ/LHUWyCMG7iHpyqrFsRvnvAytmXgaWEafat2PI9AGfRzmgi+xNzH7LRhRTcwD99CvtkNIPpg4O4iBc5bGM622YU0cAH6p9l3T9rE73bTMJnJMZSOnCruVqzXRbxdU4fDp8Gsj8SXHZwp7acEY4Q8TMsjhbOLJsMORbm70WLNOO8WmsTkcDoejy/CS4qA2BRxNSmDa6UNMKiJ71Cqy0a81sIy8z90CTiYjM/1kkcPTvYD+bcTknq6v8WOc+hNuHd4ryURfiqeVRcSc+YCYu6TknW4aeYf5mOkrKXmnmzZM8x9IjY1Xj+OOsRowzX8zwB9gCf9D1J7Gm//eUr+5fwC8RuoRjycjrTvQzX/9SJ3fLnLnucfWB9P8dwF9CYlDYZr/xgz9PY8p/7um+pc7pqjLMOV/3ivKMAXtPUeY/M8r5Ky9Q0dx6QwA5zDPb97uY7bmWs/vhdeRiql9pPziACn6fqiJ9YrCl5CjrzLNVbEOh8PhcDgcwD9/cRbHNA11OAAAAABJRU5ErkJggg==)
Then, heat produced will be ![](data:image/png;base64,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)
Now, The ratio after simplifying will be as follow:-
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPcAAABDCAYAAABA15MwAAAJ+ElEQVR4nO2dTYgdxxGAv8uDPSwsFosDEgkksAcJExtknkyisDosyPIPwqwROiiHHFZIASnBCGxwUPawWCHP2DI2EQTZYLDBNksEMlGCE9lGQYTEJPjnIiMZdFgdclgf9qCLD5tDdTOz82ame6Z7Zt5PfTCgnel5qu7pmu7qqukCRVEURVEUZXTYAxwGDgCzHcuiKEoEesB5YA04DrwEbAG/7lIoRVHCOQc8nTm3AmwDJ9sXR1GUWNxCRus0M8jofbd1aRRFicZ9ZJT+Qeb8bXP+gdYlUhQlCn3g8cy5HjJyb5h/K4oyIRxBRu3VjuVQFCUiPeAL4DrqElMyzAAnCo6lVLlDJeW0U5XTJ7/dDlUov6+g7AXgU2BXNGnHkx7F/dMeRxleq5horHKfBr5DpneXzbmfpcotmXP/NWU+A36B+Fpncn63D9xpTOrxoo+01ddI232JuK9+UlL+bVP2X8iz+X5OuVPAOvpyhaQfryDrD9tILEBauQdIn7wJ7O9GzG74HtIgW5QvyvzNlHsy59pZpAGvAZumnJLwCtImv/MouwT8ieJnsQy8kbm+SP6LtmmeQfrNfAf/d5ZZZJDaLLn+BSJv0Wxo4ngW6XgflpSZIXHFzOVc3w88gnS4j1DlznIWaZN3HOV6wBXy2xjgIPISzSr+a0HS1WedYmVqmyWkjddLyqyZMm+1ItEIcAmp8PMlZR4lmZK7UOUe5kmkTW44yp0BjhVcWwC+Qjroauq4hIz0RfSBH3pLKrL6utU2KVemNmSwXEDa+GxJmddNmSsVf3ts+Qqp8KMlZZ43ZV7x+D1V7mEeQtpko6TMbuD9kut3zW/kHa+W3Pdb4B7ycnAxMGV9bHlbpzJlalqGNP8w8jxUUuaWKfPLir89lszjZ29/SLG9nUWVe5g5EkUs6rTvkr94FgOrMGXK5VNmN8ki1WWkPufN366+EUuGPFz2NsiMyM6epiLgx04Xy+xtGwVVZG9nUeXO539Iu+zNubZM8193lSmOr1ItkCj35+Ye+7fPiz+GDHm47O1jwLfARabIw2BXce8Afy04/o2/vQ2q3EX8E2mXw5nzc4gN2MZokqdAdZVqE5ltdCmDxdrbnzC8HnEd6ec/qvnbY8tnxLW3QZW7iPeQdjmdOf8ysuDUFmlFqqtU1t5e6VCGNHn29jzyiew9ZMSeiqm4xdqBMe1tUOUuYoC0yyB1ro8odxey3Ke+UlnXXohChspgcdnbx8l/qU40TdjboMpdxGl22oU94Cr+7RqTAaIQdRVr3dzbpQwWl7296Lg+kVh7O5Z/26LKnc9hdrblOWQhrW3sNHgf8AH1lGuLevZ2TBksLv+2NSvfrPn7Y0kT9jaochexgLTLJuLyClGOumTt2x7VlSvP3p4DnmhRhjQu//YV/EN/J4Km7G1Q5S5ihsTXfQ3xGbdJ0cJVVeWy5kXapfcCfqvRsWSw+Pi3rQsyPbJP9M6xP8dtb89S3d6GxOWzp7Z0k8sG0jZnWv5/XSvSVZTLLqZZHgZebFkGy1O47WkblXYidW4iY8v/AnxMsqnefWSk/WOqzG/Mubvm+A6Zwn9E8dv59+b6n5E9vW4j/vGr5rwi3EA+5WzTLeMb+plWrrJRbRfyCesp4DkkQs1Vn9gyXMXdjy0riHJfRGZPA4ZjDRQlmKOErQzXYRH/jzbsxgcuZZ1Bpra+gSFNyFCFfcj60YtM0eeeo0gP6Tg/DTgOMGVBC4oyDjxGMrUPOQ62LbiitMXqiB9dsqqHHi0e0WlS2BhHl6zqoUeLh6IoiqIoyhjyGMlmjHWP+xTvDa4oSkf0kN1UQ1xh+1FXmDLFaMYRpSp7kOiuiY7NngRiZxw5iYSffoxs27ROcWYNZbzoIWGma8hzfwkJ/Wx63zclkBgZR95GFN4yi8QIbwO/iiOm0iHnkC2L0tiY7ZPti6P4Eppx5Gnk4efdc8fcoyP4eHMLGa3TzJB8uKGMKKEZR64g29weyblm9w2byE/spgj7Ys9myrxtzj/QukSKF6EZR+zmDHkpWuzUTT/7HG/6wOOZc3Z/vQ3UMzGSxMg4cgSxuQ/kXFtjynIzTRFHkGe72rEcSgFN7YBq+TtTlJtpiugh6XCvoy6xkaWJjCOWH5v7/sPkTtvsxgJlx1GGbdU26BfIc6hC+aKNDS4AnyK7sigjSlM7oPaAm8h2OW1vBBhCVV+9jRVYIZndrLFTQQbmt24ikXNt0Ufck18bub40chbVp4+YV9vIVlCnyU9MeAppl65GbI2n8KDJHVAvAN/Q/pZCIYT46l27cM4i09gt2t/mx87OfLb2XUJyfRf1h2Xgjcz1RXYGMzXJKMZTPIM81/mO/v9cmrK3V5CO/GCQdO0S6qtfwr0Lp11cbNstaHcrfcdRrocsfBY954PILCSr+K8FSefPqMZTrFO+tXInNJFxZBmZLmWnbCP1Vssh1FfvynoB8Dpuz0Ef/40EQV7QrvUM+xK/4Sh3Bkl1m8cC4jJdY+cmBJeQkb6ImPUJeUZNtKtlkxFMVRTb3j6IpGzJs8X+UFm6dgn11buyXkCyf3aZ58B3C2BI9gF32b42Q8hGSZndwPsl1+9S/HntqyX3xaxPyDNqol0haduyl3rrxLa3Fxi2xSx7kTf+KBPiq/fJenGMZPR0jQg+KW2rpL21z3qb4g77LvmLZzGIVZ/QeIpYcuwmWSy9bP7f8+bvKutSjREz48iDJAkM8nYh3aKbhHexcPnqXfb2MeBbZFN83xXmsk5WJ5+1TamzN+faMs1/3RW7Pll84yliyLFAotyfm3vs350qdxMZR2yitbKjbLo6yvj46q29/QnD9uh1xKTx3bw/TV5nq6sINsVTNtPGHPL82ohDiFmfNFXjKWLKsUk3CR2VQHx99Xn29jyyunsPGbHrKk+604UowntGxmwC+peRxaa2iFUfS914ihhy5GU7VcYEH1+9y94+Tr5SVWGAzLBCFMGuJg9S5/qIcrdNjPpYQuIpQuWwLsZxiuVQ8PfVu+ztRcd1HwbICyREGWzaXStHD0mmV/VbgRjEqA+Ex1OEyrFu7lXGiCq+epd/27oS36wpi50y7iMsQf1hdsYrnKObRc5Y9QmNp4ghxxZqb48VVX31Lv+2XWz0Cf3MkrUFe9TviAtGjk3E5dVFp4xVn9B4ihhy5Nnbc8ATnvcrLVPVV+/j37YuqPTI7rNzaNEiT12FmCHxXFyj/Y95YtUnNJ4ilhzWzEm7Fl+gnldEaZg6vvqncNvTNirtROqcK7bctXpbV8E3jCxnKtwTg1j1CY2niNmudjHN8jCS+1sZQar46q/ijhWwrJh7LyKj54BhX3Ma3zDJdEf0DYy5gXzK2YZP2xKzPiHxFLHbdRfyKe0p4DkkQq3NdlUURVEURVEURVEURVEURVGUKeX/LvWXY8lM224AAAAASUVORK5CYII=)
∴ ![](data:image/png;base64,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)
Thus, option (c) is correct.
Question 5.How is a voltmeter connected in the circuit to measure the potential difference between two points ?
Answer:The volt meter is always connected in parallel connection across the two points where the potential difference is to be measured in the circuit.
Question 6.A copper wire has diameter 0.5 mm and resistivity of 1.6 x 10-8
m. What will be the length of this wire to make its resistance 10
? How much does the resistance change if the diameter is doubled?
Answer:Given:
The radius of wire,
r = ![](data:image/png;base64,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)
Area of the cross-section can be calculated by,
![](data:image/png;base64,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)
The Resistivity of the resistor, ![](data:image/png;base64,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)
Resistance, R= 10![](data:image/png;base64,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)
Formula used:
Resistance, ![](data:image/png;base64,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)
Where,
ρ is the resistivity of the copper wire
L is the length of the copper wire
A is the area of the cross-section of the wire
Solving the above equation for the length
![](data:image/png;base64,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)
Putting the values in the above equation, we get
![](data:image/png;base64,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)
Thus, the length of copper wire required to make 10
resistance will be 122.5 meters.
(b) If the diameter is twice, D'=2D
Where,
D' is the new diameter
D is the initial diameter
Then, according to the question, the new diameter is twice the initial diameter.
D' = 2(0.5mm) = 1mm
Now, the new radius R' =D (Initial diameter of the cross-section)= D'/2 = 0.5 mm
As we know,
![](data:image/png;base64,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)
Putting the values in the above formula, we get
![](data:image/png;base64,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)
Thus, Resistance, R=2.5 Ω
Thus, if we twice the diameter of the copper wire the resistance become the quarter part of the initial resistance.
Question 7.The values of current I flowing in a given resistor for the corresponding values of potential difference V across the resistor are given below:
I (amperes): 0.5, 1.0, 2.0, 3.0, 4.0
V (volts): 1.6, 3.4, 6.7, 10.2, 13.2
Plot a graph between V and I plotted by using the given data is shown below:
Answer:The graph between V and I plotted by using the given data is shown below:
![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4RDaRXhpZgAATU0AKgAAAAgABAE7AAIAAAAFAAAISodpAAQAAAABAAAIUJydAAEAAAAKAAAQyOocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAERFTEwAAAAFkAMAAgAAABQAABCekAQAAgAAABQAABCykpEAAgAAAAM3NQAAkpIAAgAAAAM3NQAA6hwABwAACAwAAAiSAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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)
We know that Resistance = Slope of the Graph= ![](data:image/png;base64,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)
Thus, the resistance of the resistor is 3.4 ohms.
Question 8.When a 12 V battery is connected across an unknown resistor, there is a current of 2.5 mA in the circuit. Find the value of the resistance of the resistor.
Answer:In this problem,
The current, I = ![](data:image/png;base64,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)
Potential difference, V = 12 V
And, Resistance, R=?
And, From Ohm's law:
![](data:image/png;base64,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)
The value of the resistor is 4800 ![](data:image/png;base64,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)
Question 9.A battery of 9 V is connected in series with resistors of 0.2
, 0.3
, 0.4
, 0.5
and 12
respectively. How much current would flow through the 12
resistor?
Answer:All the resistors are connected in series.
Thus, equivalent resistance, R = 0.2
+ 0.3
+ 0.4
+ 0.5
+ 12 = 13.4 ![](data:image/png;base64,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)
Potential difference, V = 9 V
And, Current, I=?
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Since in series connection, the current throughout the circuit is same. Therefore, 0.67 A will flow through the 12
resistor.
Question 10.How many 176
resistors in parallel are required to carry 5 A on a 220 V line?
Answer:Here, Potential difference = is 220 V
And the current, I = 5 A.
![](data:image/png;base64,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)
Thus, the resistance of the circuit is 44 ohms.
Now, we need to find the number of
resistors should be connected in parallel to obtain a resultant resistance of 44
. Suppose the number of 176
resistors required is ‘n’.
Then,
![](data:image/png;base64,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)
Thus, 4 resistors of 176
each should be connected in parallel.
Question 11.Show how you would connect three resistors, each of resistance 6
, so that the combination has a resistance of (i) 9
, and (ii) 4
.
Answer:(i) In order to get a resistance of 9
from three resistors of 6
each, we connect two 6
resistors in parallel and then this parallel combination is connected in series with the third 6
resistor .
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)
For parallel connection: ![](data:image/png;base64,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)
Or R= 3![](data:image/png;base64,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)
And for series connection: R= 3
+ 6
= 9 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAATCAYAAAByUDbMAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAFlSURBVDjLxZRPToNAFMYfNXFF3GP6zmBgFi7cdEHoGKs7klbCTlkYwqKadGHMwI5tb1BdcgTLUeQC2ivYOoPUDn+KMWkqyRcW8+Y373vzAURRBLsS7AXGH4WrU1fS+RNMbPItfODvJddnScbwpQArv8Ie70yCAAuxEWkwltdCl1wU0JU+erqqAkugycQ9JgAZAH7QgOlNXTPmarzmTQDJiF1uhV0TeBZFQJxZ26BDhwzyui5NvThWa7A49lTahTQ/0QkHbTAWUP17FLiQHVTbz6oFLVazrbC8M4T5TmBCAcUxD9eyOtiGGzdym0jnjTNbd3eO8Kp0+6nteUdNoIRnbGgAzxq+Vx3UUi+AfQ4Up1aBAuQQmMkgOWulGyKWf7v+bPLwIk1kGyI6RVh/aogV3DTCiuSvNiKZy5hWy6EktPz7+m16tsphZ7ygtxE5pdPpYW4xsQ9MDU7K69DTzAD3+wv6d9gX76DcReUnwZ0AAAAASUVORK5CYII=)
(ii) In order to get a resistance of 4
, their are multiple cases
(a) 1st Case
From three resistors of 6
each, we connect all the three 6
resistors in parallel:
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Or R= 2![](data:image/png;base64,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)
Then, Net Resistance R= 2
+ 2
= 4
.
(b)2nd Case
We connect two resistors of 6 Ω in series and another resistor of 6 Ω in parallel to them
R= 6 Ω + 6Ω= 12Ω
Then Net Resistance ![](data:image/png;base64,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)
Then R= 4 Ω
![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4RCCRXhpZgAATU0AKgAAAAgABAE7AAIAAAAFAAAISodpAAQAAAABAAAIUJydAAEAAAAKAAAQcOocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAERFTEwAAAAB6hwABwAACAwAAAhiAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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)
Question 12.Several electric bulbs designed to be used on a 220 V electric supply line are rated 10 W each. How many bulbs can be connected in parallel with each other across the two wires of 220 V line if the maximum allowable current is 5 A ?
Answer:First we will calculate the resistance R of one bulb.
We know, ![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAUCAMAAABh7EcdAAAAAXNSR0ICQMB9xQAAAANQTFRFAAAAp3o92gAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAADUlEQVQoz2NgGAXYAAABGAABizFjXgAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
Therefore, resistance of one bulb is 4840![](data:image/png;base64,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)
We will now calculate the total resistance of the circuit by using Ohm’s Law:
![](data:image/png;base64,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)
Thus, the total resistance of the circuit is 44
.
Now, we need to find out the number of 4840
bulbs should be connected in parallel to obtain a total resistance of 44
. Suppose the number of 4840
bulbs required is x. Then:
![](data:image/png;base64,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)
=110
Thus, 110 bulbs can be connected in parallel in this circuit.
Question 13.A hot plate of an electric oven connected to a 220 V line has two resistance coils A and B, each of 24
resistance, which may be used separately, in series or in parallel. What are the currents in the three cases?
Answer:Case (i): When each coil is used separately
Here, Potential difference, V = 220 V
Resistance of a coil, R = 24![](data:image/png;base64,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)
Using Ohm’s Law, the current passing through one coil is given as,
![](data:image/png;base64,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)
Case (ii) Calculation of current when the two coils are connected in series
When the two coils of 24
each are connected in series, then their combined resistance will be R= 24
+ 24
= 48 ![](data:image/png;base64,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)
Potential difference, V = 220 V
And, Resistance, R = 48 Q
Again, Current passing through both coils connected in series, is given as:
![](data:image/png;base64,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)
Case (iii) Calculation of current when the two coils are connected in parallel
When the two coils of 24
each are connected in parallel, then their combined resistance will be given as:
![](data:image/png;base64,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)
Here, Potential difference, V = 220 V
Resistance of two coils in parallel connection, R = 12
(Two coils in parallel)
Now, Current, I = ![](data:image/png;base64,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)
Question 14.Compare the power used in the 2
resistor in each of the following circuits:
(i) a 6 V battery in series with 1
and 2
a resistors.
(ii) a 4 V battery in parallel with 12
and 2
resistors.
Answer:(i) In the First Case:
Potential difference, V = 6 V
And, Net Resistance, R= 1
+ 2
= 3
(Resistors are connected in series)
Now, by Ohm’s law: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Thus, the current flowing in the circuit containing 1
and 2
resistors in series is 2 A. In a series circuit, the same current flows throughout the circuit. So, the current flowing through the 2
resistor is also 2A. Now, we know that the current (in 2
resistor) is 2 A and its resistance is 2
.
Now, Power used in 2
resistor is given as:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOUAAAAgCAYAAADt7L8RAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAARwSURBVHja7Vw7UuQwENUBOMBShcnmAKCNNzQOiLdqmCKjiCgnxJQhm4QLkBEScILlBNxgA27AHXZLNrKNRmq1bI+smnnBq6I8H9Qtve7X3QLx8PAgAABIB3ACAICUAACAlECLCymehRD/hMg+i7I6gU9ASmBG3K/kuVzdn6ufb/LsVhwVb9fr9QF8A1ICCaCqLg9Pxemfy6o6hD9ASsitREgp5aqCL0BKyK1EUOb5b2RJkHLn5VZVFicyL6/mVRbZo09RqGCX5Te3IABIudNySxEyy4qXuTP5en19UGTZi4uYipBCXjzrNRfL6heIAFJaUctTom5MWW7VAeP47CkVae1SFY2PVX2uIT/m9Onmer7wFTT2mpR1dD0Sb1YHfUHXdnOQsi+3OGuNLc1UM8rln831DmtY1RkuYB+UP2P7gWtrrSqE+LTtlbYzxpljBwtHkLCfRfmxrMrF5vPOF3UQF+Kjfc3olWxGfPVmYxFtB3SGCOaSW961RmoKNVkpe7cdPlNKdpsRTszQPWgO/ul7rEzItZXjg/6hjU3MhpCdgtBroQJcS2Jjb9rnjrNYv27ZTzvzjTf2I0JMJ1Fyy0XK2GulusJVuVwsy2phyxIhWUzXq8VP8coltPZDrGzJtZUbXNqMGbnjXq/PRi5ive1ZNNbanUV7mbCSsrI9Z5GyT5BtbXKzWfwM4iJlf63bJiXlL9+6Q/yofKPerw8q97O1TwMPNdXlDu2Am7aGBMxO4sadT5tnh1JCnDPnel7bJy8evY0e6pDpCOdyZjfk94DIbFOQsvs++ruGrncswZrDlv0NsVMTwRWRaRvDmzk28g0ZSZm2hsj3IVJ/ij3drBN5/muDCFPCqucuLrFIGaNO83VfOaTs1yIxZNsQKaqzXpBfejaGKIpQn1LBYMiM2LSVGzDH1t/Tlk48Utps0115s+xQ781lfufiEqObFKdNPZiUM3ZeQ0kZOsu0zRzbWouxH2NI+d3HA7Ktw1ZuadFmnhlucZnlAtd+s7zQUwPXc9f3jK6RppIOYzOlr6jehtQJqfF8Q32y2WGF3865SEnZ2u6Th2yhPYap9tRs3Llkqa/hU96XP86O5ZPym3k2fbeuJiNlUvI11jgkIFNSs0xKDtk+w802c8lXn60+Yg4h5DYbd+aYhNXwyfO7fiPH9XznSRka2WKR0nZIy1xeUbZSUpdr41BSjmn0ULaad4NtNpqfj3mf2BUsGsUS2PBxzmf9wZQ1b0malJa1htYCg0lJjGW8korwMZUlzdqf2uCQCM8hn4+YPlv7N3lcMtz2HTH7BObob8i81zWK4nbD6QZPpIz5fSNoYrrWajrt+8WD7ZDTpyyoGse1yb4rWNYGFyUDIwVYjq0+UnL3Nl7nddjvdzVyuFk/qkTdRaT6d56xb/QA0wFOmEDCcm58RF9X5LuvAEiZXLZMLSP1L/IDIOWeZst0/iuCkq56Rob9ASn3l5jEBePY8I1bAJByb5CCZAy9WwuAlAAAgJQAAFICADAC/wH+ry3Blzr0wQAAAABJRU5ErkJggg==)
(ii) In the Second Case:
Here, 4 V battery is attached across the parallel combination of 12
and 2
resistors, so the potential difference across the 2
resistor will also be 4 V. Because in parallel connection
Voltage is same.
Now, Potential difference, V= 4 V
And Resistance, R = 2![](data:image/png;base64,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)
![](data:image/png;base64,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)
So, Power used in 2
resistor, P=
=![](data:image/png;base64,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)
Thus, the power used in the 2
resistor in the second case is also 8W.
From both the cases we can say that the 2
resistor uses equal power in both the circuits.
Question 15.Two lamps, one rated 100 W at 220 V and the other 60 W at 220 V are connected in parallel to electron mains supply. What current is drawn from the line if the supply voltage is 220 V?
Answer:Given the power of the two lamps, we will calculate the resistances R1 and R2 of two lamps separately.
![](data:image/png;base64,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)
Now, The two lamps of resistances 484
and 806.7
are connected in parallel.
So, the combined resistance of two lamps can be calculated as follows:
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Total resistance, R= 302.5![](data:image/png;base64,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)
Current drawn from the line can now be calculated by using Ohm's law as follows:
![](data:image/png;base64,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)
Thus, the current drawn from the line is 0.72 A
Question 16.Which uses more energy, a 250 W TV set in 1hr or a 1200 W toaster in 10 minutes ?
Answer:(i) For TV set:
Power, P= 250W=![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAM0AAAAwCAYAAACysP6uAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAASQSURBVHja7Zw/UuMwFMZ1AA6wzGCq5QCs9gwmBRcgmXQMBcO4oWYMXRouQEdJsTfgBHuDLbgBd2BxvAmSrD9Pfza2oq/4ZsCJHUt6P0vv+Ruxh4cHBkEQXegECAI0EARoIAjQQBCggciac/bMGH9btu0h+mOPoFmtrg5mR+yVMfbRq3qfNe2pOQg232MfVX1zK37etstDzthb/7k9WIa/259z0TYnw+Nf9yT/xqeOZq9Xq9XBLjrwfsHPde22t03fDzm2H9BsBq6qXoYDMgSnbWanFWPv4mDyxf25CszmWB9g7qfsTV3drq/H58/a44agWH+unPO/pAa4Cxq5DfY+yKH9gEYC4eLkomlPdHCogdHNMrZgWc9CwgBvA80xsFtQleD4ClR90C04b3e97DH1TQw0ObUf0DgGUQwMaZbRPPl051CDRnyqijOX7fj6fvj8cdcdGAuNtLwVHia5tB/QWAOj+iMuz7ZLBdPS7F8wqYPbL9HMOdIASuISpTuu/lYO0PTn//itPkRyaT+gsSyz1KC4vr7+bkv0NwmyHprhcXPOoCS8x2dPs5/sl3i8+27N67sxkt8YaNbnVrMX3X3n0n5AYwoKw8Daqkix0Jiu2f1tOj5GBwZDs+SXripXDu0HNI5Kms+MZFqe9UHjXp6pCXFz33w7O+ZP3RNaTYjnvHqk3uM0oHGX8nNpP6DRQOCzTpagiSwEDBLfur4TE13T8Vxmmu27F8dsM/X2AxoHME3NL21PNLXkGVpy1ibEylNZzKXGTICjcxrHuVNvP6ARg12pjIkVG92yTVe9UZdovrOMCT75Pse1pMRWz0wl5FzaP6bGaj8dGCHxHNg2LG/EZddAWANNiW53bV43l+MOmmx5MbVPZ5HpQJFzHP35U23/MBZo4xtr06JYkkx9nsKWhOkWigbGxyaV0qbl+6I8lS2pmAFeD6ghl8KLwYiZ1jNnTWnTokKT2pZU1CDrwOk6Hu84wmeZ2Oqo6Voum5but0yWJFvuGGJLKm6wRXAADD2flfTZf7E2qeFM42fT0kFjsiRJECawJRUZHJuOAjCRD59Ix4dtGeayaanQuJwrKW1JgAYAjApNqE1LgoZgSdJdI9SWhOUZwEm6PPOxScXYtIZLOIJzPpEtSf6H0mEZKbQQsG/94NtPuyoExNi0xN+iWpKkxD/CllTWDGPoVN/Bg8JLzrY+97Vp+VqS5KpcuC0Jgw+Fl50JNildLpLKphViSdLBLt+Xe5bE4ENJwDFZWlRoUti0YixJtkSfakvCwEOQp9AJEARoIGiPoKHuRjkVue6XYounWuf3fSdSQOOp0N0oxxLlfim2eKp1fp93IgU0iSotucw0tvulvKOgvscoYSdSQFM4NJS34dQ35qXsRApoSoeGYIunWudL2YkU0BQODcXhS3UBl7ITKaABNJOBRvwuduIENNktz0RbPNU6X8pOpIAGhYDJFAIGiT924gQ0U4Sm0xRKztqCAHbiBDRThYZii6fuMFrCTqSAJkA+u1FOQZT7peweSt1hdJ93IgU0EARo0AkQBGggCNBA0HT0FwDJZXAqsqqSAAAAAElFTkSuQmCC)
Time, t = 1 h
So, Electric energy, E= P x t = 0.25Kw x 1 h = 0.25 kWh
(ii) For toaster:
Power, P= 250W= ![](data:image/png;base64,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)
Time, t= 10 min= ![](data:image/png;base64,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)
So, Electric energy, E= P x t= 1.2 kW x
= 0.20kWh
From the above calculations, it is clear that the TV set uses more energy (0.25 kWh) whereas toaster uses less energy (0.20 kWh).
Question 17.An electric heater of resistance 8
draws 15 A from the service mains for 2 hours. Calculate the rate at which heat is developed in the heater.
Answer:Given
Resistance, R =8Ω
Current, I=15 A
Time period,T = 2 hours
Power, P is the rate at which the heat is developed by the heater
Formula used:
Power, P= I2 R
Where
I is the current
R is the resistance
Putting the values in the above equation, we get
H = 15 Χ 15 Χ 8 = 1800 W
Thus, the rate at which heat is developed in the heater is 1800 joules per second.
Question 18.Explain the following:
(a) Why is the tungsten used almost exclusively for the filament of electric lamps?
(b) Why are the conductors of electric heating devices such as bread toasters and electric irons made of an alloy rather than a pure metal ?
(c) Why is the series arrangement not used for domestic circuits?
(d) How does the resistance of a wire vary with its area of cross-section?
(e) Why are copper and aluminium wires usually employed for electricity transmission?
Answer:(a) Tungsten is used almost exclusively for making the filaments of electric lamps and electric bulbs because it has very high melting point nearly 3380°C due to which the tungsten filament can be kept white-hot without melting away.
(b) The coils (or heating elements) of toasters and electric irons are made of an alloy rather than a pure metal because the resistivity of an alloy is much higher than that a pure metal, and an alloy does not undergo oxidation easily even at high temperature, when it is red hot but metals can get easily oxidized at higher temperatures.
(c) The series arrangement is not used for domestic circuits because of the following disadvantages:
(i) In series arrangement, the current throughout the circuit is same. If one electrical appliance stops working due to some defect, then all other appliances also stops working (because the whole circuit is broken).
(ii) In series arrangement, all the electrical appliances can have only one switch due to which they cannot be turned 'on' or 'off' independently.
(iii) In series arrangement, all the appliances do not get the same voltage (220 V) as that of the power supply line (because the line voltage is shared by all the appliances). Due to this, the appliances do not work properly.
(iv) In series arrangement of electrical appliances, the overall resistance of the circuit increases too much because in series the net resistance is the addition of all the resistances. Due to this the current from power supply is low. Because of this, all the appliances of different power ratings cannot draw sufficient current for their proper working.
(d) The resistance of a wire is inversely proportional to its area of cross-section i.e. Thus, when the area of cross-section of wire increases (or thickness of wire increases), then its resistance decreases. Similarly, when the area of cross-section of wire decreases (or thickness of wire decreases), then its resistance increases.
(e) Copper and aluminium wires are usually employed for transmission of electricity because copper and aluminium are good conductors of electric current due to their low electrical resistivity. ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADUAAAAvCAYAAABDq4KNAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAALdSURBVGje7ZnRTuJAFIZP4da410rnHaSTfQMzlLjuXTcC6dVuGkNML0AzF4YU7kh0n2FZL30EAw+yKk8gj4CyM20HRqAFjChD5uIELNierz3nP/8M0Gq1YNti64A0lIbSUEskCWCwyAKMjK2AugXINEr57wxqhMhZXXmodtvbKSC4Y0DPWwMlIvDtPAIYaCgNpaE0lIbSUJvoKC6rhziCOr0AcLJvgpp4rXmx+KTvGWUMf9h1h5Ow7t0g2FsZquniI2FNGN+zdFL23uo7lOaUdOnjOrb92hi2bh+wY08czKV0XzkoVscWAvTP9oO8fPyMoHP+BHGl+W2VC41mS9r4cKgoefwo1y/1nF1iQg8APdn15kFSY08Sj9Y/HOiUoAu5lHEpOF4XWKLlt03ognVyIxL0POdLwTS6PCFkV2tJQBUMHZE4l2D2molukPEi/18Zo6ukG7MWKErdfQugH4vFkNXNC0tqBKh457XbO0kn40DYbR6Jv6s2qqFi8To8F650PrWnghI+Dkss7qfo7qeLQxC4e4T4P+aXcXK5zhkn2bfEQig2G/6CaXfFU+ESb3BxYH2QBoXZF+Q+odTJWWCET2nZ/nk9k5aPVKi4n3pyuYQJAzyCVb5ZNChjAZB6ED+47tef08IQq+HHCEUk5TCYlmxRgg4Ncss7gMn0l4F5+AT/WrtQCGt0YgFTPDQ4rF5ieUtKlKCkiCvdZWkTZZimoO8KFVujV3UqX5iXIFOx+/GckVROGUehcqibeIrQKAvEd22T/KeSUNGicdZsKwvFLVw4MwH3kxaLSgHxgc2M8G9CcGMroHgfMR9Z52Mm9JOSjVMWKuwjXLme503V3CILjbHVdXzf5J6STHlT5aB4H5VwpiM7HWPBb1XK9NHUiqGvJBR/QlEfla/m7XKlbfxsqv3Jhhs1Juk5Ht0VnznsuPj9N19qsNfbjBJQM6sFVAj3RaZXCfJn2qVrqA2K/9elC24tH0fHAAAAAElFTkSuQmCC)
A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R', then the ratio R/R' is:
A. 1/25
B. 1/5
C. 5
D. 25
Answer:
The resistance of wire is R. This wire is cut into five equal pieces as a result resistance of each piece of wire will be R⁄5.Now, when these five pieces are connected in parallel, the equivalent resistance for the combination is R’. We can write,
(Assume that each piece of wire is named R1, R2, R3, R4, R5)
Thus, the correct answer is: Option (d)
Question 2.
Which of the following terms does not represent electrical power in a circuit?
A. I2R
B. IR2
C. VI
D. V2/R
Answer:
the electrical power is not represented as IR2
Question 3.
An electric bulb is rated 220 V and 100 W. When it is operated on 110 V, the power consumed will be:
A. 100 W
B. 75 W
C. 50 W
D. 25 W
Answer:
The bulb parameters are as given below:
Power, P = 100W
Potential difference, V = 220V
Then Resistance, R = ?
Now,
This resistance of the bulb will remain constant i.e. 484
Now, when we operate this bulb on 110 V, then,
Power, P =?
Potential difference, V = 110V
And, resistance, R = 484
P =
P = =
= 25 W
Thus, the correct answer is: (d) 25 W.
Question 4.
Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then in parallel in a circuit across the same potential difference. The ratio of heat produced in series and parallel combination would be:
A. 1 : 2
B. 2 : 1
C. 1 : 4
D. 4 : 1
Answer:
Suppose the resistance of each one of the two wires is R.
Case (i) When both wires are connected in series. Then, net resistance will be R+
R = 2R.
Current(I)=
Then, heat produced will be ( As H = I2 X R X T)
Case (ii) When both wires are connected in parallel. Then, net resistance will be
According to Ohms Law:
Current(I)=
Then, heat produced will be
Now, The ratio after simplifying will be as follow:-
Thus, option (c) is correct.
Question 5.
How is a voltmeter connected in the circuit to measure the potential difference between two points ?
Answer:
The volt meter is always connected in parallel connection across the two points where the potential difference is to be measured in the circuit.
Question 6.
A copper wire has diameter 0.5 mm and resistivity of 1.6 x 10-8 m. What will be the length of this wire to make its resistance 10
? How much does the resistance change if the diameter is doubled?
Answer:
Given:
The radius of wire,
r =
Area of the cross-section can be calculated by,
The Resistivity of the resistor,
Resistance, R= 10
Formula used:
Resistance,
Where,
ρ is the resistivity of the copper wire
L is the length of the copper wire
A is the area of the cross-section of the wire
Solving the above equation for the length
Putting the values in the above equation, we get
Thus, the length of copper wire required to make 10 resistance will be 122.5 meters.
(b) If the diameter is twice, D'=2D
Where,
D' is the new diameter
D is the initial diameter
Then, according to the question, the new diameter is twice the initial diameter.
D' = 2(0.5mm) = 1mm
Now, the new radius R' =D (Initial diameter of the cross-section)= D'/2 = 0.5 mm
As we know,
Putting the values in the above formula, we get
Thus, Resistance, R=2.5 Ω
Thus, if we twice the diameter of the copper wire the resistance become the quarter part of the initial resistance.
Question 7.
The values of current I flowing in a given resistor for the corresponding values of potential difference V across the resistor are given below:
I (amperes): 0.5, 1.0, 2.0, 3.0, 4.0
V (volts): 1.6, 3.4, 6.7, 10.2, 13.2
Plot a graph between V and I plotted by using the given data is shown below:
Answer:
The graph between V and I plotted by using the given data is shown below:
We know that Resistance = Slope of the Graph=
Question 8.
When a 12 V battery is connected across an unknown resistor, there is a current of 2.5 mA in the circuit. Find the value of the resistance of the resistor.
Answer:
In this problem,
The current, I =
Potential difference, V = 12 V
And, Resistance, R=?
And, From Ohm's law:
The value of the resistor is 4800
Question 9.
A battery of 9 V is connected in series with resistors of 0.2, 0.3
, 0.4
, 0.5
and 12
respectively. How much current would flow through the 12
resistor?
Answer:
All the resistors are connected in series.
Thus, equivalent resistance, R = 0.2 + 0.3
+ 0.4
+ 0.5
+ 12 = 13.4
Potential difference, V = 9 V
And, Current, I=?
Since in series connection, the current throughout the circuit is same. Therefore, 0.67 A will flow through the 12 resistor.
Question 10.
How many 176 resistors in parallel are required to carry 5 A on a 220 V line?
Answer:
Here, Potential difference = is 220 V
And the current, I = 5 A.
Thus, the resistance of the circuit is 44 ohms.
Now, we need to find the number of resistors should be connected in parallel to obtain a resultant resistance of 44
. Suppose the number of 176
resistors required is ‘n’.
Then,
Thus, 4 resistors of 176 each should be connected in parallel.
Question 11.
Show how you would connect three resistors, each of resistance 6, so that the combination has a resistance of (i) 9
, and (ii) 4
.
Answer:
(i) In order to get a resistance of 9 from three resistors of 6
each, we connect two 6
resistors in parallel and then this parallel combination is connected in series with the third 6
resistor .
For parallel connection:
Or R= 3
And for series connection: R= 3 + 6
= 9
(ii) In order to get a resistance of 4 , their are multiple cases
(a) 1st Case
From three resistors of 6 each, we connect all the three 6
resistors in parallel:
Then, Net Resistance R= 2+ 2
= 4
.
(b)2nd Case
We connect two resistors of 6 Ω in series and another resistor of 6 Ω in parallel to them
R= 6 Ω + 6Ω= 12Ω
Then Net Resistance
Then R= 4 Ω
Question 12.
Several electric bulbs designed to be used on a 220 V electric supply line are rated 10 W each. How many bulbs can be connected in parallel with each other across the two wires of 220 V line if the maximum allowable current is 5 A ?
Answer:
First we will calculate the resistance R of one bulb.
We know,
Therefore, resistance of one bulb is 4840
We will now calculate the total resistance of the circuit by using Ohm’s Law:
Thus, the total resistance of the circuit is 44.
Now, we need to find out the number of 4840 bulbs should be connected in parallel to obtain a total resistance of 44
. Suppose the number of 4840
bulbs required is x. Then:
=110
Thus, 110 bulbs can be connected in parallel in this circuit.
Question 13.
A hot plate of an electric oven connected to a 220 V line has two resistance coils A and B, each of 24resistance, which may be used separately, in series or in parallel. What are the currents in the three cases?
Answer:
Case (i): When each coil is used separately
Here, Potential difference, V = 220 V
Resistance of a coil, R = 24
Using Ohm’s Law, the current passing through one coil is given as,
Case (ii) Calculation of current when the two coils are connected in series
When the two coils of 24 each are connected in series, then their combined resistance will be R= 24
+ 24
= 48
Potential difference, V = 220 V
And, Resistance, R = 48 Q
Again, Current passing through both coils connected in series, is given as:
Case (iii) Calculation of current when the two coils are connected in parallel
When the two coils of 24 each are connected in parallel, then their combined resistance will be given as:
Here, Potential difference, V = 220 V
Resistance of two coils in parallel connection, R = 12 (Two coils in parallel)
Now, Current, I =
Question 14.
Compare the power used in the 2resistor in each of the following circuits:
(i) a 6 V battery in series with 1 and 2
a resistors.
(ii) a 4 V battery in parallel with 12 and 2
resistors.
Answer:
(i) In the First Case:
Potential difference, V = 6 V
And, Net Resistance, R= 1 + 2
= 3
(Resistors are connected in series)
Now, by Ohm’s law:
Thus, the current flowing in the circuit containing 1 and 2
resistors in series is 2 A. In a series circuit, the same current flows throughout the circuit. So, the current flowing through the 2
resistor is also 2A. Now, we know that the current (in 2
resistor) is 2 A and its resistance is 2
.
Now, Power used in 2 resistor is given as:
(ii) In the Second Case:
Here, 4 V battery is attached across the parallel combination of 12 and 2
resistors, so the potential difference across the 2
resistor will also be 4 V. Because in parallel connection
Voltage is same.
Now, Potential difference, V= 4 V
And Resistance, R = 2
So, Power used in 2 resistor, P=
=
Thus, the power used in the 2 resistor in the second case is also 8W.
From both the cases we can say that the 2 resistor uses equal power in both the circuits.
Question 15.
Two lamps, one rated 100 W at 220 V and the other 60 W at 220 V are connected in parallel to electron mains supply. What current is drawn from the line if the supply voltage is 220 V?
Answer:
Given the power of the two lamps, we will calculate the resistances R1 and R2 of two lamps separately.
Now, The two lamps of resistances 484 and 806.7
are connected in parallel.
So, the combined resistance of two lamps can be calculated as follows:
Total resistance, R= 302.5
Current drawn from the line can now be calculated by using Ohm's law as follows:
Thus, the current drawn from the line is 0.72 A
Question 16.
Which uses more energy, a 250 W TV set in 1hr or a 1200 W toaster in 10 minutes ?
Answer:
(i) For TV set:
Power, P= 250W=
Time, t = 1 h
So, Electric energy, E= P x t = 0.25Kw x 1 h = 0.25 kWh
(ii) For toaster:
Power, P= 250W=
Time, t= 10 min=
So, Electric energy, E= P x t= 1.2 kW x = 0.20kWh
From the above calculations, it is clear that the TV set uses more energy (0.25 kWh) whereas toaster uses less energy (0.20 kWh).
Question 17.
An electric heater of resistance 8draws 15 A from the service mains for 2 hours. Calculate the rate at which heat is developed in the heater.
Answer:
Given
Resistance, R =8Ω
Current, I=15 A
Time period,T = 2 hours
Power, P is the rate at which the heat is developed by the heater
Formula used:
Power, P= I2 R
Where
I is the current
R is the resistance
Putting the values in the above equation, we get
H = 15 Χ 15 Χ 8 = 1800 W
Thus, the rate at which heat is developed in the heater is 1800 joules per second.
Question 18.
Explain the following:
(a) Why is the tungsten used almost exclusively for the filament of electric lamps?
(b) Why are the conductors of electric heating devices such as bread toasters and electric irons made of an alloy rather than a pure metal ?
(c) Why is the series arrangement not used for domestic circuits?
(d) How does the resistance of a wire vary with its area of cross-section?
(e) Why are copper and aluminium wires usually employed for electricity transmission?
Answer:
(a) Tungsten is used almost exclusively for making the filaments of electric lamps and electric bulbs because it has very high melting point nearly 3380°C due to which the tungsten filament can be kept white-hot without melting away.
(b) The coils (or heating elements) of toasters and electric irons are made of an alloy rather than a pure metal because the resistivity of an alloy is much higher than that a pure metal, and an alloy does not undergo oxidation easily even at high temperature, when it is red hot but metals can get easily oxidized at higher temperatures.
(c) The series arrangement is not used for domestic circuits because of the following disadvantages:
(i) In series arrangement, the current throughout the circuit is same. If one electrical appliance stops working due to some defect, then all other appliances also stops working (because the whole circuit is broken).
(ii) In series arrangement, all the electrical appliances can have only one switch due to which they cannot be turned 'on' or 'off' independently.
(iii) In series arrangement, all the appliances do not get the same voltage (220 V) as that of the power supply line (because the line voltage is shared by all the appliances). Due to this, the appliances do not work properly.
(iv) In series arrangement of electrical appliances, the overall resistance of the circuit increases too much because in series the net resistance is the addition of all the resistances. Due to this the current from power supply is low. Because of this, all the appliances of different power ratings cannot draw sufficient current for their proper working.
(d) The resistance of a wire is inversely proportional to its area of cross-section i.e. Thus, when the area of cross-section of wire increases (or thickness of wire increases), then its resistance decreases. Similarly, when the area of cross-section of wire decreases (or thickness of wire decreases), then its resistance increases.
(e) Copper and aluminium wires are usually employed for transmission of electricity because copper and aluminium are good conductors of electric current due to their low electrical resistivity.