Question

NCERT Solutions Class 10 Science Chapter 12 Electricity explores all concepts related to Electricity. In this solution, concepts are discussed by the subject expert and these solutions are precisely made for students to understand all the topics in simple language. In our solution, we have solved all kinds of questions related to NCERT books. Solutions of intext questions and exercise questions are also provided in it. These solutions are made comprehensible using diagrams, flow charts, shortcuts, tips, and tricks. Overall these solutions are easy to understand.  

In this particular chapter of NCERT Solutions Class 10 Science Chapter 12 Electricity all the solutions are discussed with in-depth analysis to clear all kinds of queries of students. Important topics which we need to learn in this chapter are Electric charge, Rules of Electric charge, Electric Current, Electric Potential Difference, Electric circuit, Different Symbols used in Electric Circuit, Ohm’s law, Experiments to verify Ohm’s Law, Factors on which Resistance of conductor depends, Electrical Resistivity, Resistance in series, Resistance in Parallel, electric power, the heating effect of electric current, application of the heating effect of electric current, the difference between resistance and resistivity, ammeter connected in series, a voltmeter connected in parallel, the difference between open and closed circuits, why does ammeter have low resistance, why does voltmeter have high resistance, least count of ammeter and voltmeter.

It is highly advised by our subject matter expert to students to go through our NCERT Solutions Class 10 Science Chapter 12 Electricity for a better understanding of all topics of the NCERT book. Our syllabus is based on the latest syllabus proposed by CBSE. We have articulated our question-answer solution in such a way it helps one learn and revise the concepts in the least possible time.

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Answer 1

NCERT Solutions Class 10 Science Chapter 12 Electricity

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:

option (d) 25 is correct.

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 

 

2. Which of the following terms does not represent electrical power in a circuit?

(a) I²R

(b) IR²

(c) VI

(d) V² /R

Answer:

Correct option is (b) IR²

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  V and  W. When it is operated on  V, the power consumed will be –

(a) 100 W

(b) 75 W

(c) 50 W

(d) 25 W

Answer:

option (d) is correct

Energy consumed by bulb 

= \(P=\frac{V^2}R\) ⇒ R = \(\frac{V^2}P\)

 Here, V = 220 V and P = 100 W

R = \(\frac{220^2}{100}\) = 484 \(\Omega\)

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

\(P=\frac{V^2}R=\frac{110^2}{484}=\frac{12100}{484}\) = 25 W

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

Answer:

Option (c) is correct.

Heat produced in the circuit is inversely proportional to the resistance R. Let R_S and R_P 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

R_S = 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. 

5. How is a voltmeter connected in the circuit to measure the potential difference between two points?

Answer:

To measure the potential difference, a voltmeter should be connected in parallel. 

6. A copper wire has diameter . 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?

Answer:

Resistance (R) of a copper wire of length l and cross-section A is given by the expression,

\(R=\rho\frac{l}A\)

Where, \(\rho\) is resistivity of copper = 1.6 × 10^–8 Ω m

R = 10 Ω, radius of wire r = 0.5/2 mm = 0.25 mm = 0.00025 m

If the diameter (radius) is doubled, the new radius r = 0.5 mm = 0.0005 m

A = π r² = 3.14 x (0.0005)² = 0.0000000785m²

 So, the new resistance will be

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. 

Answer:

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) 

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:

According to Ohm’s law, V = IR

9. A battery of 9 V is connected in series with resistors of 0.2 Ω, 0.3 Ω, 0.4 Ω, 0.5 Ω and 12 Ω, respectively. How much current would flow through the  Ω resistor?

Answer:

Total resistance of resistors when connected in series is given by

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.

Answer 2

10. How many  176 Ω resistors (in parallel) are required to carry 5 A on a 220 V line?

Answer:

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 = \(\frac{V}{I}=\frac{220}5\) = 44 \(\Omega\)

Now for x number of resistors of resistance 176 \(\Omega\), the equivalent resistance of the resistors connected in parallel is 44 \(\Omega\). 

Therefore, 4 resistors of 176 \(\Omega\) 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.

Answer:

(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:

Total resistance in parallel is given by 

Now R₁₂ and 6 \(\Omega\) are connected in series, so the net resistance is given by

R = R₁₂ + 6 \(\Omega\) = 3 \(\Omega\) + 6 \(\Omega\) = 9 \(\Omega\)

(ii). To get total  4\(\Omega\) resistance from three  6\(\Omega\) resistors, we should connect two resistors in series and the third resistor in parallel with the resultant. The combination is given as follows:

Total resistance in series is given by

R₁₂ = R₁ + R₂ = 6 \(\Omega\) + 6 \(\Omega\) = 12 \(\Omega\)

Now R₁₂ and 6 \(\Omega\) are connected in parallel, so the net resistance is given by

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?

Answer:

For one bulb:

Power P = 10 W and Potential difference V = 220 V

Using the relation for R, we have

R = \(\frac{V^2}P=\frac{220^2}{10}\) = 4840 \(\Omega\)

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 = 44 \(\Omega\)

Now, for x number of bulbs of resistance 176\(\Omega\), the equivalent resistance of the resistors connected in parallel is  44\(\Omega\)

 Therefore, 110 bulbs of  4840 \(\Omega\) 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?

Answer:

Given that:

Potential difference V = 220 V and resistance of each coil R =  24\(\Omega\)

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 =  24\(\Omega\) + 24\(\Omega\) = 48\(\Omega\)

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

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\(\Omega\) resistor in each of the following circuits:

(i) a 6 V battery in series with 1\(\Omega\) and 2\(\Omega\) resistors, and (ii) a 4 V battery in parallel with 12\(\Omega\) and 2\(\Omega\) resistors.

Answer:

Given that:

Potential difference, V = 6 V

(i). 1 \(\Omega\) and  2 \(\Omega\) resistors are connected in series. Therefore, equivalent resistance of the circuit, R = 1 + 2 = 3\(\Omega\)

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 = I²R = (2)² x 2 = 8 W

(ii). 1 \(\Omega\) and 2 \(\Omega\) resistors are connected in parallel.

⇒ I = V/R = 6/3 = 2A

In parallel combination, the voltage in the circuit remains constant. Therefore power is given by

P = \(\frac{V^2}R=\frac{4^2}2\) = 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?

Answer:

For the lamp one:

Power P₁ = 100 W and Potential difference V = 220 V

Therefore, 

\(I_1=\frac{P_1}{V}\) = 100/220 = 0.455 A

For the lamp two:

Power P₂ = 60 W and Potential difference V = 220 V

Therefore,

\(I_1=\frac{P_2}V\) = 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  minutes?

Answer:

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. 

Answer 3

17. An electric heater of resistance 8\(\Omega\) draws 15 A from the service mains  hours. Calculate the rate at which heat is developed in the heater.

Answer:

Heat developed in the heater is given by H = I²Rt

Where, I = 15 A, R = 8 \(\Omega\) and time t = 2 hours

The rate at which heat is developed is given by

\(H=\frac{I^2RT}t=I^2R\) = (15)² x 8 = 1800 J/s

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?

Answer:

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 \(\propto \frac1A\)

e) Copper and aluminium wires have low resistivity. They are good conductors of electricity. Hence, they are usually employed for electricity transmission.

19. What does an electric circuit mean?

Answer:

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. 

20. Define the unit of current.

Answer:

The unit of electric current is ampere (A). When 1C of charge flows through a conductor in 1 s, it called 1 ampere (A) current.I = Q/t

21. Calculate the number of electrons constituting one coulomb of charge.

Answer:

We know that one electron possesses a charge of 1.6 × 10⁻¹⁹ C.

So, the number of electrons constituting one coulomb of charge is 6 × 10¹⁸

Answer 4

22. Name a device that helps to maintain a potential difference across a conductor.

Answer:

A cell, battery, power supply, etc. helps to maintain a potential difference across a conductor.

23. What is meant by saying that the potential difference between two points is  V?

Answer:

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.

24. How much energy is given to each coulomb of charge passing through a  V battery?

Answer:

\(Potential\,Difference=\frac{Work\,done}{Charge}\)

or Work done (or Energy) = Potential Difference × Charge

So, Work done = 6 Volt × 1 Coulomb = 6 Joules

25. On what factors does the resistance of a conductor depend?

Answer:

The resistance of a conductor depends upon the following factors:

Ø Length of the conductor

Ø Cross-sectional area of the conductor

Ø Material of the conductor

Ø Temperature of the conductor. 

26. 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:

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.

27. 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?

Answer:

According to the Ohm’s law V = IR

If the resistance remains constant, V is directly proportional to I.

V \(\propto\) I

Now, if potential difference is reduced to half of its value, the current also become half of its original value.

28. Why are coils of electric toasters and electric irons made of an alloy rather than a pure metal?

Answer:

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.

29. Use the data in Table . to answer the following –

(a) Which among iron and mercury is a better conductor?

(b) Which material is the best conductor?

Answer:

(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. 

30. Draw a schematic diagram of a circuit consisting of a battery of three cells of 2 V each, a  Ω resistor, an 5 Ω resistor, 8 Ω resistor, and a 12 Ω resistor, plug key, all connected in series.

Answer:

The required schematic diagram is given below:

Answer 5

31. Redraw the circuit of Question 30, 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?

Answer : 

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 ⟹ = 6/25 = 0.24

Now for the 12 Ω 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.

32. 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.

Answer :

(a). The net resistance in parallel is given by

\(\frac{1}{R}= \frac{1}{R_1}+\frac{1}{R_2}\)

Here, 1 = 1 Ω and 2 = 106 Ω 

So,

(b). The net resistance in parallel is given by

\(\frac{1}{R}= \frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}\)

Here, ₁ = 1 Ω, ₂ = 10³ Ω and ₃ = 10⁶ Ω

So,

33. 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? 

Answer : 

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

\(\frac{1}{R}= \frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}\)

Here, ₁ = 100 Ω, ₂ = 50 Ω and ₃ = 500 Ω 

So,

Now, using Ohm’s law V = IR, we have

Hence, the resistance of electric iron is 31.25 Ω and current through it is 7.04 A.

34. What are the advantages of connecting electrical devices in parallel with the battery instead of connecting them in series? 

Answer : 

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.

35. 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? 

Answer : 

(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

Now, the resultant ₁₂ and 2 Ω resistors are in series. So the net resistance

= ₁₂ + 2 Ω = 2 + 2 = 4 Ω

(b). To get total resistance 1 Ω, connect 2 Ω, 3 Ω and 6 Ω resistors in parallel. 

The net resistance in parallel is given by

\(\frac{1}{R}= \frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}\)

Here, ₁ = 2 Ω, ₂ = 3 Ω and ₃ = 6 Ω 

So,

36. 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? 

Answer : 

Connecting resistors in series always gives maximum resistance and parallel gives minimum resistance.

(a). The highest total resistance is given by

= ₁ + ₂ + ₃ + ₄ = 4 Ω + 8 Ω + 12 Ω + 24 Ω = 48 Ω

(b). The lowest total resistance is given by

37. Why does the cord of an electric heater not glow while the heating element does? 

Answer : 

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.

38. Compute the heat generated while transferring 96000 coulomb of charge in one hour through a potential difference of 50 V. 

Answer : 

According to Joule’s law of heating, the amount of heat produced is given by

H = VIt

Where, 

V = 50 V

and t = 1 hour = 60 × 60 seconds 

So,

39. An electric iron of resistance 20 Ω takes a current of 5 A. Calculate the heat developed in 30 s.

 Answer :

According to Joule’s law of heating, the amount of heat produced is given by 

H = VIt 

Where, 

V = IR = 5A × 20 Ω = 100 V 

I = 5 A 

and t = 30 seconds 

So,

= 100 × 5 × 30  

= 15000 = 1.5 × 10⁴  

40. What determines the rate at which energy is delivered by a current? 

Answer : 

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.

41. An electric motor takes 5 A from a 220 V line. Determine the power of the motor and the energy consumed in 2 h. 

Answer : 

Power of the electric motor is given by

P = VI 

Where, V = 220 V and I = 5 A 

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