NCERT Solution for Class 10 Science Chapter 12 Electricity
Chapter Name | NCERT Solution for Class 10 Science Chapter 12 Electricity |
Topics Covered | - NCERT Intext Questions
- NCERT Exercise Solution
|
Related Study | - NCERT Solution for Class 10 Science
- NCERT Revision Notes for Class 10 Science
- Important Questions for Class 10 Science
- MCQ for Class 10 Science
- NCERT Exemplar Questions For Class 10 Science
|
NCERT Exercises Solution
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
Solution
Resistance of a piece of wire is directly proportional to its length. If the piece of wire has a resistance R and the wire is cut into five equal parts.
The resistance of each part = R/5
All the five parts are connected in parallel. Hence, equivalent resistance (R′) is given as
Hence, the option (d) is correct.
2. Which of the following terms does not represent electrical power in a circuit?
(a) I2R
(b) IR2
(c) VI
(d) V2/R
Solution
We know that electric power is given by P = VI … (i)
So, the option (c) is correct.
According to Ohm’s law, V = IR … (ii)
Now putting the value of V from (ii) in (i), we get
Power P = (IR) × I = I2R
So, the option (a) is correct.
Now putting the value of I from (ii) in (i), we get
Power P = V(V/R) = V2/R
So, the option (d) is correct.
Hence, the option (b) does not represent electrical power in a circuit.
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
Solution
Energy consumed by bulb = P = V2/R
⟹ 𝑅 = V2/P
Here, V = 220 V and P = 100 W
R = (220)2/100 = 484Ω
The resistance of the bulb remains constant if the supply voltage is reduced to 110 V. If the bulb is operated on 110 V, then the energy consumed by it is given by the expression for power
P = V2/R = (110)2/484 = 12100/484 = 25 W
Hence, the option (d) is correct.
4. Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then parallel in a circuit across the same potential difference. The ratio of heat produced in series and parallel combinations would be –
(a) 1:2
(b) 2:1
(c) 1:4
(d) 4:1
Solution
Heat produced in the circuit is inversely proportional to the resistance R. Let Rs and RP be the equivalent resistances of the wires if connected in series and parallel respectively. Let R be the resistance of each wire. If the resistors are connected in parallel, the net resistance is given by
If the resistors are connected in series, the net resistance is given by
Rs = R + R = 2R
Hence, for same potential difference V, the ratio of heat produced in the circuit is given by
Therefore, the ratio of heat produced in series and parallel combinations is 1:4.
Hence, the option (c) is correct.
5. How is a voltmeter connected in the circuit to measure the potential difference between two points?
Solution
To measure the potential difference, a voltmeter should be connected in parallel.
6. A copper wire has diameter 0.5 mm and resistivity of 1.6 × 10–8 Ω m. What will be the length of this wire to make its resistance 10 Ω? How much does the resistance change if the diameter is doubled?
Solution
Resistance (R) of a copper wire of length l and cross - section A is given by the expression,
Where, ρ is resistivity of copper = 1.6 × 10-8 Ωm
R = 10 Ω, radius of wire r = 0.5/2 mm = 0.25 mm = 0.00025 m
Now R'/R = 2.5/10 = 1/4
⟹ R' = (1/4)R
Hence, the new resistance will become 1/4 times the original resistance.
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 and calculate the resistance of that resistor.
Solution
The plot between voltage and current is called VI characteristic. The voltage is plotted on x-axis and current is plotted on y-axis.
The slope of the line gives the value of resistance (R)
slope = 1/R = BC/AC = 2/6.8
⟹ 𝑅 = 6.8/2 = 3.4 Ω
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.Solution
According to Ohm’s law, V = IR
⟹ R = V/I
Here, V = 12V and I = 2.5 mA = 0.0025 A
Therefore, R = 12/0.0025 = 4800 Ω = 4.8 kΩ
9. A battery of 9 V is connected in series with resistors of 0.2 Ω, 0.3 Ω, 0.4 Ω, 0.5Ω and 12 Ω, respectively. How much current would flow through the 12 Ω resistor?Solution
Total resistance of resistors when connected in series is given by
R = R
1 + R
2 + R
3 + R
4 + R
5 ⟹ 𝑅 = 0.2 Ω + 0.3 Ω + 0.4 Ω + 0.5 Ω + 12 Ω = 13.4 Ω
According to Ohm’s law, V = IR
⟹ 𝐼 = V/R = 9/13.4 = 0.67 A
There is no current division occurring in a series circuit. So, the current through the 12 Ω resistor will be same as 0.67 A.
Solution
Let the total number of resistors be x.
Given that:
Current I = 5 A and Potential Difference V = 220 V
According to Ohm’s law, V = IR
⟹ R = V/I = 220/5 = 44 Ω
Now for x number of resistors of resistance 176 Ω, the equivalent resistance of the resistors connected in parallel is 44 Ω.
Therefore, 4 resistors of 176 Ω are required to draw the given amount of current.
11. Show how you would connect three resistors, each of resistance 6 Ω, so that the combination has a resistance of (i) 9 Ω, (ii) 4 Ω.
Solution
(i) To get total 9 Ω resistance from three 6 Ω resistors, we should connect two resistors in parallel and the third resistor in series with the resultant. The combination is given as follows:
(ii) To get total 4 Ω resistance from three 6 Ω resistors, we should connect two resistors in series and the third resistor in parallel with the resultant. The combination is given as follows:
12. Several electric bulbs designed to be used on a 220 V electric supply line, are rated 10 W. How many lamps can be connected in parallel with each other across the two wires of 220 V line if the maximum allowable current is 5 A?
Solution
For one bulb:
Power P = 10 W and Potential difference V = 220 V
Using the relation for R, we have
Let the total number of bulbs be x.
Given that:
Current I = 5 A and Potential Difference V = 220 V
According to Ohm’s law, V = IR
⟹ R = V/I = 220/5 = 44Ω
Now, for x number of bulbs of resistance 176 Ω, the equivalent resistance of the resistors connected in parallel is 44 Ω.
⟹ 1/44 = x/4840
⟹ x = 4840/44 = 110
Therefore, 110 bulbs of 4840 Ω are required to draw the given amount of current.
13. A hot plate of an electric oven connected to a 220 V line has two resistance coils A and B, each of 24 Ω resistance, which may be used separately, in series, or in parallel. What are the currents in the three cases?
Solution
Given that :
Potential difference V = 220 V and resistance of each coil R = 24 Ω
When the coil is used separately, the current in the coil is given by
I = V/R = 220/24 = 55/6 = 9.16 A
When the two coils are connected in series, the net resistance is given by
R = R1 + R2 = 24Ω + 24 Ω = 48 Ω
Now, the current in the coil is given by
I = V/R = 220/48 = 55/12 = 4.58 A
When the two coils are connected in parallel, the net resistance is given by
1/R = 1/24 + 1/24 = 2/24 = 1/12
⟹ 𝑅 = 12 Ω
Now, the current in the coil is given by
I = V/R = 220/12 = 55/3 = 18.33 A
14. Compare the power used in the 2 Ω resistor in each of the following circuits: (i) a 6 V battery in series with 1 Ω and 2 Ω resistors, and (ii) a 4 V battery in parallel with 12 Ω and 2 Ω resistors.
Solution
Given that:
Potential difference, V = 6 V
(i) 1 Ω and 2 Ω resistors are connected in series. Therefore, equivalent resistance of the circuit, R = 1 + 2 = 3 Ω
According to Ohm’s law,
V = IR
⟹ I = V/R = 6/3 = 2 A
In series combination, the current in the circuit remains constant. Therefore power is given by
𝑃 = 𝐼
2 𝑅 = (2)
2 × 2 = 8 𝑊
(ii) 1 Ω and 2 Ω resistors are connected in parallel.
⟹ 𝐼 = 𝑉/𝑅 = 6/3 = 2 𝐴
In parallel combination, the voltage in the circuit remains constant. Therefore power is given by
𝑃 = V2𝑅 = (4)2 × 2 = 8 𝑊
Hence, in both the cases power remains same as 8W.
15. Two lamps, one rated 100 W at 220 V, and the other 60 W at 220 V, are connected in parallel to electric mains supply. What current is drawn from the line if the supply voltage is 220 V?
Solution
For the lamp one:
Power P1 = 100 W and Potential difference V = 220 V
Therefore,
𝐼
1 = 𝑃
1/𝑉 = 100/220 = 0.455 𝐴
For the lamp two:
Power P1 = 60 W and Potential difference V = 220 V
Therefore,
𝐼
2 = 𝑃
2/𝑉 = 60/220 = 0.273 𝐴
So, the net current drawn from the supply is given by
𝐼 = 𝐼1 + 𝐼2 = 0.455 + 0.273 = 0.728 𝐴
16. Which uses more energy, a 250 W TV set in 1 hr, or a 1200 W toaster in 10 minutes?
Solution
Energy consumed by an electrical appliance is given by H = Pt
For the TV set:
Power W = 250 W and time t = 1 hour = 3600 seconds
So, energy consumed H = 250 × 3600 = 900000 J
For the toaster:
Power W = 1200 W and time t = 10 minutes = 600 seconds
So, energy consumed H = 1200 × 600 = 720000 J
Hence, TV set uses more energy than toaster.
17. An electric heater of resistance 8 Ω draws 15 A from the service mains 2 hours. Calculate the rate at which heat is developed in the heater.
Solution Heat developed in the heater is given by H = I2Rt
Where, I = 15 A, R = 8 Ω and time t = 2 hours
The rate at which heat is developed is given by
18. Explain the following.a) Why is the tungsten used almost exclusively for 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?
Solution
a) The melting point and resistivity of tungsten are very high. It does not burn readily at a high temperature. The electric lamps glow at very high temperatures. Hence, tungsten is mainly used as heating element of electric bulbs.
b) The conductors of electric heating devices such as bread toasters and electric irons are made of alloy because resistivity of an alloy is more than that of metals. It produces large amount of heat and do not burn easily.
c) There is voltage division in series circuits. Each component of a series circuit receives a small voltage for a large supply voltage. As a result, the amount of current decreases and the device becomes hot. Hence, series arrangement is not used in domestic circuits.
d) Resistance (R) of a wire is inversely proportional to its area of cross-section
(A): R ∝ 1/A
e) Copper and aluminium wires have low resistivity. They are good conductors of electricity. Hence, they are usually employed for electricity transmission.
NCERT Intext Questions
Page 200
1. What does an electric circuit mean ?
Solution
An electric circuit is the pathway in which current can flow. It consists of electric devices, switching devices, source of electricity, etc. that are connected by conducting wires.
2. Define the unit of current.
Solution
The unit of electric current is ampere (A). When 1 C or charge flows through a conductor in 1 s, it called 1 ampere (A) current.
I = Q/t
3. Calculate the number of electrons constituting one coulomb of charge.
Solution
We know that one electron possesses a charge of 1.6 × 10-19 C.
Number of electron = Total charge/Charge of 1 electron
= 1/1.6 × 10-19 = 6.25 × 1018
So, the number of electrons constituting one coulomb of charge is 6 × 1018 .
Page 202
1. Name a device that helps to maintain a potential difference across a conductor.
Solution
A cell, battery, power supply, etc. helps to maintain a potential difference across
a conductor.
2. What is meant by saying that the potential difference between two points is 1 V?
Solution
When 1 J of work is required to move a charge of 1 C from one point to another, then it is said that the potential difference between the two points is 1 V.
V = W/Q
1V = 1j/1C
3. How much energy is given to each coulomb of charge passing through a 6 V battery ?
Solution
Potential Difference = Work done/Charge
or Work done (or Energy) = Potential Difference × Charge
So, Work done = 6 Volt × 1 Coulomb = 6 Joules
Page 209
1. On what factors does the resistance of a conductor depend?
Solution
The resistance of a conductor depends upon the following factors:
- Length of the conductor
- Cross-sectional area of the conductor
- Material of the conductor
- Temperature of the conductor.
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?
Solution
Resistance (R) is inversely proportional to the area of cross-section (A) of the wire. So, thicker the wire, lower is the resistance of the wire and vice-versa .
Therefore, current can flow more easily through a thick wire than a thin wire.
R ∝ 1/A
3. Let the resistance of an electrical component remains 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?
Solution
According to the Ohm’s law V = IR
If the resistance remains constant, V is directly proportional to I.
V ∝ 1
Now, if potential difference is reduced to half of its value, the current also become
half of its original value.
4. Why are coils of electric toasters and electric irons made of an alloy rather than a
pure metal?
Solution
The resistivity of an alloy is higher than the pure metal and it does not corrode easily. Moreover, even at high temperatures, the alloys do not melt readily.
Hence, the coils of heating appliances such as electric toasters and electric irons are made of an alloy rather than a pure metal.
5. Use the data in Table 12.2 to answer the following –
(a) Which among iron and mercury is a better conductor?
(b) Which material is the best conductor?
Solution
(a) Resistivity of iron (10.0 × 10-8 Ω m) is lesser than that of the mercury (94.0 × × 10-8 Ω m). So, iron is good conductor as compared to mercury.
(b) Silver has lowest resistivity, so it is the best conductor.
Page 213
1. Draw a schematic diagram of a circuit consisting of a battery of three cells of 2 V each, a 5 Ω resistor, an 8 Ω resistor, and a 12 Ω resistor, and a plug key, all connected in series.
SolutionThe required schematic diagram is given below :
2. Redraw the circuit of Question 1, putting in an ammeter to measure the current through the resistors and a voltmeter to measure the potential difference across the 12 Ω resistor. What would be the readings in the ammeter and the voltmeter?
Solution
Resisters are connected in series.
So, the net resistance in the circuit = 5 Ω + 8 Ω + 12 Ω = 25 Ω
Net potential = 6 V
Using Ohm’s law V = IR, we have
6 = I × 25 ⟹ 𝐼 = 6/25 = 0.24 𝐴𝑚𝑝𝑒𝑟𝑒
Now for the 12Ω resistor, current = 0.24 A
So, using Ohm's law V = 0.24 × 12 V = 2.88 V
Hence, the reading in the ammeter is 0.24 and voltmeter is 2.88.
Page 216
1. Judge the equivalent resistance when the following are connected in parallel -
(a) 1 Ω and 106 Ω, (b) 1 Ω and 103 Ω, and 106 Ω.
Solution
(a) The net resistance in parallel is given by
1/R = 1/R1 + 1/R2
Here R1 = 1 Ω and R2 = 106 Ω.
So,
2. An electric lamp of 100 Ω, a toaster of resistance 50 Ω, and a water filter of resistance 500 Ω 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?
Solution
Given that the electric lamp of 100 Ω, a toaster of resistance 50 Ω and water filter of resistance 500 Ω are connected in parallel. The net resistance in parallel is given by
3. What are the advantages of connecting electrical devices in parallel with the
battery instead of connecting them in series?
Solution
In parallel there is no division of voltage among the appliances. The potential difference across each appliance is equal to the supplied voltage and the total effective resistance of the circuit can be reduced by connecting electrical appliances in parallel.
4. How can three resistors of resistances 2 Ω, 3 Ω, and 6 Ω be connected to give a total resistance of (a) 4 Ω, (b) 1 Ω?
Solution
(a) To get total resistance 4 Ω, connect 3 Ω and 6 Ω resistors in parallel and 2 Ω resistance in series with the resultant.
Since, 3 Ω and 6 Ω resistors in parallel, so the net resistance
⟹ 𝑅12 = 2/1 = 2 Ω
Now, the resultant R12 and 2Ω resistors are in series. So the the net resistance
R = R12 + 2Ω = 2 + 2 = 4Ω
(b) To get total resistance 1 Ω, 2Ω, 3Ω and 6Ω resistors in parallel.
The net resistance in parallel is given by
5. What is (a) the highest, (b) the lowest total resistance that can be secured by
combinations of four coils of resistance 4 Ω, 8 Ω, 12 Ω, 24 Ω?
Solution
Connecting resistors in series always gives maximum resistance and parallel gives minimum resistance.
(a). The highest total resistance is given by
Page 218
1. Why does the cord of an electric heater not glow while the heating element does?
Solution
The heating element of an electric heater is a resistor. According to Joule’s law of heating, the amount of heat produced by it is proportional to its resistance.
H = I2Rt
The resistance of the element of an electric heater is very high. As current flows through the heating element, it becomes too hot and glows red. On the other hand, the resistance of the cord is low. It does not become red when current flows through it.
2. Compute the heat generated while transferring 96000 coulomb of charge in one hour through a potential difference of 50 V . Solution
According to Joule's law of heating, the amount of heat produced is given by
H = Vlt
Where,
V = 50 V
I = Charge/time = 9600 coulomb/1hr = 9600/60 × 60 = (80/3)A
and t = 1 hour = 60 × 60 seconds
So,
H = 50 × 80/3 × 60 × 60
4800000 J = 4.8 × 106 J
3. An electric iron of resistance 20 Ω takes a current of 5 A. Calculate the heat developed in 30 s.Solution
According to Joule's law of heating, the amount of heat produced is given by
H = Vlt
where,
V = IR = 5A × 20 Ω = 100 V
I = 5 A
and t = 30 seconds
So, H = 100× 5 × 30 J
= 15000 J = 1.5 × 104 J
Page 220
1. What determines the rate at which energy is delivered by a current ?
Solution
The rate of consumption of electric energy in an electric appliance is called electric power. Hence, the rate at which energy is delivered by a current is the power of the appliance.
2. An electric motor takes 5 A from a 220 V line. Determine the power of the motor
and the energy consumed in 2 h.
Solution
Power of the electric motor is given by
P = VI
Where, V = 220 V and I = 5A
So, Power P = 220 × 5 = 1100 W
Now, the energy consumed = Power × time
Where, P = 1100 W
t = 2 hours = 2 × 60 × 60 seconds = 7200 seconds
So, the energy consumed E = 1100 × 7200 J = 7920000 J
