Science · Textbook solutions

Electricity

Every solved example, exercise, and miscellaneous question, in the order the textbook teaches them. Plus every board question asked from this chapter. · 62 questions

11.1 Electric Current and Circuit

4 q

Solved Examples

Worked · 1

11.1 Eg.1 $A current of 0.5 A is drawn by a filament of an electric bulb for 10 minutes. Find the amount of electric charge that flows through the circuit.$

Questions

Practice · 3

IT 11.1 Q1 $What does an electric circuit mean?$
IT 11.1 Q2 $Define the unit of current.$
IT 11.1 Q3 $Calculate the number of electrons constituting one coulomb of charge.$

11.2 Electric Potential and Potential Difference

4 q

Solved Examples

Worked · 1

11.2 Eg.2 $How much work is done in moving a charge of 2 C across two points having a potential difference 12 V?$

Questions

Practice · 3

IT 11.2 Q1 $Name a device that helps to maintain a potential difference across a conductor.$
IT 11.2 Q2 $What is meant by saying that the potential difference between two points is 1 V?$
IT 11.2 Q3 $How much energy is given to each coulomb of charge passing through a 6 V battery?$

11.4-11.5 Ohm's Law and the Factors on which Resistance Depends

10 q

Solved Examples

Worked · 4

11.3 Eg.3 $\Omega$
11.3 Eg.4 $The potential difference between the terminals of an electric heater is 60 V when it draws a current of 4 A from the source. What current will the heater draw if the potential difference is increased to 120 V?$
11.3 Eg.5 $\Omega$
11.3 Eg.6 $l$

Questions

Practice · 6

IT 11.3 Q1 $On what factors does the resistance of a conductor depend?$
IT 11.3 Q2 $Will current flow more easily through a thick wire or a thin wire of the same material, when connected to the same source? Why?$
IT 11.3 Q3 $Let the resistance of an electrical component remains constant while the potential difference across the two ends of the component decreases to half of its former value. What change will occur in the current through it?$
IT 11.3 Q4 $Why are coils of electric toasters and electric irons made of an alloy rather than a pure metal?$
Use the data in Table 11.2 to answer the following –
IT 11.3 Q5 (a) $Which among iron and mercury is a better conductor?$
IT 11.3 Q5 (b) $Which material is the best conductor?$

11.6.1 Resistors in Series

3 q

Solved Examples

Worked · 1

11.4 Eg.7 $\Omega$

Questions

Practice · 2

IT 11.4 Q1 $\Omega$
IT 11.4 Q2 $\Omega$

11.6.2 Resistors in Parallel

10 q

Solved Examples

Worked · 2

11.5 Eg.8 $R_1$
11.5 Eg.9 $R_1 = 10\,\Omega$

Questions

Practice · 8

Judge the equivalent resistance when the following are connected in parallel –
IT 11.5 Q1 (a) $\Omega$
IT 11.5 Q1 (b) $\Omega$
IT 11.5 Q2 $\Omega$
IT 11.5 Q3 $What are the advantages of connecting electrical devices in parallel with the battery instead of connecting them in series?$
How can three resistors of resistances 2 $\Omega$ , 3 $\Omega$ , and 6 $\Omega$ be connected to give a total resistance of
IT 11.5 Q4 (a) $\Omega$
IT 11.5 Q4 (b) $\Omega$
What is (a) the highest, (b) the lowest total resistance that can be secured by combinations of four coils of resistance 4 $\Omega$ , 8 $\Omega$ , 12 $\Omega$ , 24 $\Omega$ ?
IT 11.5 Q5 (a) $The highest total resistance$
IT 11.5 Q5 (b) $The lowest total resistance$

11.7 Heating Effect of Electric Current

5 q

Solved Examples

Worked · 2

11.6 Eg.10 $An electric iron consumes energy at a rate of 840 W when heating is at the maximum rate and 360 W when the heating is at the minimum. The voltage is 220 V. What are the current and the resistance in each case?$
11.6 Eg.11 $\Omega$

Questions

Practice · 3

IT 11.6 Q1 $Why does the cord of an electric heater not glow while the heating element does?$
IT 11.6 Q2 $Compute the heat generated while transferring 96000 coulomb of charge in one hour through a potential difference of 50 V.$
IT 11.6 Q3 $\Omega$

11.8 Electric Power

4 q

Solved Examples

Worked · 2

11.7 Eg.12 $An electric bulb is connected to a 220 V generator. The current is 0.50 A. What is the power of the bulb?$
11.7 Eg.13 $An electric refrigerator rated 400 W operates 8 hour/day. What is the cost of the energy to operate it for 30 days at Rs 3.00 per kW h?$

Questions

Practice · 2

IT 11.7 Q1 $What determines the rate at which energy is delivered by a current?$
IT 11.7 Q2 $An electric motor takes 5 A from a 220 V line. Determine the power of the motor and the energy consumed in 2 h.$

Exercises

22 q

Ex 11 Q1 $R$
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Ex 11 Q2 $Which of the following terms does not represent electrical power in a circuit?$
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Ex 11 Q3 $An electric bulb is rated 220 V and 100 W. When it is operated on 110 V, the power consumed will be -$
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Ex 11 Q4 $Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then parallel in a circuit across the same potential difference. The ratio of heat produced in series and parallel combinations would be -$
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Ex 11 Q5 $How is a voltmeter connected in the circuit to measure the potential difference between two points?$
Ex 11 Q6 $1.6 \times 10^{-8}\,\Omega\,\text{m}$
Ex 11 Q7 $I$
Ex 11 Q8 $When a 12 V battery is connected across an unknown resistor, there is a current of 2.5 mA in the circuit. Find the value of the resistance of the resistor.$
Ex 11 Q9 $\Omega$
Ex 11 Q10 $\Omega$
Ex 11 Q11 $\Omega$
Ex 11 Q12 $Several electric bulbs designed to be used on a 220 V electric supply line, are rated 10 W. How many lamps can be connected in parallel with each other across the two wires of 220 V line if the maximum allowable current is 5 A?$
Ex 11 Q13 $\Omega$
Ex 11 Q14 $\Omega$
Ex 11 Q15 $Two lamps, one rated 100 W at 220 V, and the other 60 W at 220 V, are connected in parallel to electric mains supply. What current is drawn from the line if the supply voltage is 220 V?$
Ex 11 Q16 $Which uses more energy, a 250 W TV set in 1 hr, or a 1200 W toaster in 10 minutes?$
Ex 11 Q17 $\Omega$
Explain the following.
Ex 11 Q18 (a) $Why is the tungsten used almost exclusively for filament of electric lamps?$
Ex 11 Q18 (b) $Why are the conductors of electric heating devices, such as bread-toasters and electric irons, made of an alloy rather than a pure metal?$
Ex 11 Q18 (c) $Why is the series arrangement not used for domestic circuits?$
Ex 11 Q18 (d) $How does the resistance of a wire vary with its area of cross-section?$
Ex 11 Q18 (e) $Why are copper and aluminium wires usually employed for electricity transmission?$

$I$ (amperes)	0.5	1.0	2.0	3.0	4.0
$V$ (volts)	1.6	3.4	6.7	10.2	13.2

What the board has asked from this chapter

Questions per paper · 67 papers · 2022 to 2026

2026

33 q

30 $The correct way to connect an ammeter and a voltmeter in an electric circuit is :$
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Electric Current and Circuits
31 $I$
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Ohm's Law
33 (A) $A fuse in electric circuit is rated 4 A. Can it be used with an electric heater of rating 2 kW, 200 V ? Explain your answer.$
Heating Effect of Electric Current
36 $(a) Name a device which is used to : (i) Maintain a constant potential difference in a circuit. (ii) Change the electric current in an electric circuit. (b) When the potential difference between the terminals of an electric heater is 110 V, a current of 5 A flows through it. What will be the value of current flowing through it when the potential difference is increased to 220 V ?$
Ohm's Law
34 (a) $7\,\Omega$
Resistance and Resistivity
34 $(a) State the law which gives the relation between the electric current flowing through a given conductor and the potential difference applied across it. (b) Draw V-I graph for a given conductor as per the law stated in above question (a).$
Ohm's Law
34 $(a) Define volt, the unit of potential difference. (b) Calculate the work done required to move an electron between two points A and B located at a potential difference of 100 V in an electric field.$
Potential Difference
34 $What do the symbols given below represent in an electric circuit ? Write one function of each. (i) Symbol (i) as printed; see the attached figure. (ii) Symbol (ii) as printed; see the attached figure.$
Electric Current and Circuits
37 $V - I$
Ohm's Law
34 (b) $An electric heater is rated 220 V; 11 A. Calculate the power consumed if the heater is operated at 200 V.$
Electric Power and Energy
37 $Consider the given electric circuit : Calculate the following : (a) Total resistance of the circuit (b) The electric current drawn from the battery (c) Potential difference between points P and Q$
Resistors in Series and Parallel

I

$I$ (Amperes)	$0{\cdot}4$	$0{\cdot}8$	$1{\cdot}2$	$1{\cdot}6$	$2{\cdot}0$
$V$ (Volts)	$1{\cdot}2$	$2{\cdot}4$	$3{\cdot}6$	$4{\cdot}8$	$6{\cdot}0$

Ohm's Law

37 $8\,\Omega$
Resistors in Series and Parallel
Swati, a class 10 student, observes that when she passes close to the refrigerator in her kitchen, she feels the heat, although the things kept inside the refrigerator are cool.
38 (a) $Describe the cause of heating in the above-mentioned case.$
Heating Effect of Electric Current
Three students Shweta, Ayesha and Samridhi were performing an experiment to understand the factors on which the resistance of a conductor depends. Each one of them completed electric circuit with the help of a cell, an ammeter, a plug key and wire. Shweta put nichrome wire of length ‘l’ in the circuit and after plugging the key, noted current in the ammeter. Ayesha put nichrome wire of same thickness but twice the length i.e. ‘2*l*’ in the circuit and after plugging the key, noted current in the ammeter. Samridhi took copper wire of length ‘l’ and same thickness in the circuit and after plugging the key, noted current in the ammeter.
38 (a) $If the ammeter reading is X ampere with nichrome wire of length ‘ l ’, then what will be the ammeter reading if the length of nichrome wire is doubled with same area of cross-section ?$
Resistance and Resistivity
Swati, a class 10 student, observes that when she passes close to the refrigerator in her kitchen, she feels the heat, although the things kept inside the refrigerator are cool.
38 (b) $I$
Heating Effect of Electric Current
Three students Shweta, Ayesha and Samridhi were performing an experiment to understand the factors on which the resistance of a conductor depends. Each one of them completed electric circuit with the help of a cell, an ammeter, a plug key and wire. Shweta put nichrome wire of length ‘l’ in the circuit and after plugging the key, noted current in the ammeter. Ayesha put nichrome wire of same thickness but twice the length i.e. ‘2*l*’ in the circuit and after plugging the key, noted current in the ammeter. Samridhi took copper wire of length ‘l’ and same thickness in the circuit and after plugging the key, noted current in the ammeter.
38 (b) $What happens to the ammeter reading if the area of cross-section of nichrome wire is doubled, keeping the length of wire ‘ l ’ the same ?$
Resistance and Resistivity
Swati, a class 10 student, observes that when she passes close to the refrigerator in her kitchen, she feels the heat, although the things kept inside the refrigerator are cool.
38 (c) (i) $Write any two practical applications of heating effect of electric current.$
Heating Effect of Electric Current
Three students Shweta, Ayesha and Samridhi were performing an experiment to understand the factors on which the resistance of a conductor depends. Each one of them completed electric circuit with the help of a cell, an ammeter, a plug key and wire. Shweta put nichrome wire of length ‘l’ in the circuit and after plugging the key, noted current in the ammeter. Ayesha put nichrome wire of same thickness but twice the length i.e. ‘2*l*’ in the circuit and after plugging the key, noted current in the ammeter. Samridhi took copper wire of length ‘l’ and same thickness in the circuit and after plugging the key, noted current in the ammeter.
38 (c) $Define ‘resistivity’. Write its SI unit. Compare the resistivity of an alloy with its constituents metals.$
Resistance and Resistivity
Swati, a class 10 student, observes that when she passes close to the refrigerator in her kitchen, she feels the heat, although the things kept inside the refrigerator are cool.
38 (c) (ii) $Define the commercial unit of electric energy and express it in Joules (J).$
Electric Power and Energy
Three students Shweta, Ayesha and Samridhi were performing an experiment to understand the factors on which the resistance of a conductor depends. Each one of them completed electric circuit with the help of a cell, an ammeter, a plug key and wire. Shweta put nichrome wire of length ‘l’ in the circuit and after plugging the key, noted current in the ammeter. Ayesha put nichrome wire of same thickness but twice the length i.e. ‘2*l*’ in the circuit and after plugging the key, noted current in the ammeter. Samridhi took copper wire of length ‘l’ and same thickness in the circuit and after plugging the key, noted current in the ammeter.
38 (c) OR $Give reason : (i) Tungsten is used almost exclusively for making the filament of electric lamps. (ii) Conductors of bread-toasters are made of an alloy rather than a pure metal.$
Heating Effect of Electric Current
39 (A) $\mathrm{R_2}$
Resistors in Series and Parallel
39 (A) $V-I graph for a nichrome wire is shown in the diagram. (i) Prove that the graph follows Ohm’s law and calculate the resistance of nichrome wire from the given V-I graph. (ii) (I) Calculate the equivalent resistance of the combination of resistors connected in the given circuit. (II) Find the value of the total current drawn from the battery.$
Resistors in Series and Parallel
39 (a) $2\,\Omega$
Resistors in Series and Parallel
39 (a) $3\,\Omega$
Resistors in Series and Parallel
39 (A) $\mathrm{R_1}$
Resistors in Series and Parallel
39 (a) $(i) Due to change in length and area of cross-section of a conductor, resistance of conductor changes while resistivity does not change. Why ? (ii) Conductors of electric toasters and electric iron are made of an alloy rather than a pure metal. Why ? (iii) Define the S.I. unit of electric current.$
Resistance and Resistivity
39 (b) $8\,\Omega$
Resistors in Series and Parallel
39 (b) $(R_A : R_B)$
Electric Power and Energy
39 (b) $R_1$
Ohm's Law
39 (B) $4\,\Omega$
Resistance and Resistivity
39 (B) $(i) Define the SI unit of power. Express the electric power of an electric appliance in terms of potential difference and current flowing through it. (ii) In a house, 3 bulbs of 100 W each, are lit for 5 hours daily and an electric heater of 1.0 kW is used for half an hour daily. Calculate the total energy consumed in a month of 30 days and its cost at the rate of ₹ 3.60 per kWh. (iii) Convert the commercial unit of electric energy into Joule (J).$
Electric Power and Energy
39 (B) $55\,\Omega$
Electric Power and Energy

2025

46 q

12 $R'$
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Resistors in Series and Parallel
13 $An electric bulb is rated 220 V; 11W. The resistance of its filament when it glows with a power supply of 220 V is :$
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Electric Power and Energy
13 $A wire of length ‘ l ’ is gradually stretched so that its length increases to 3*l*. If its original resistance is R, then its new resistance will be :$
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Resistance and Resistivity
14 $The resistivity of a wire made of an alloy is generally :$
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Resistance and Resistivity
14 $An electric bulb is connected to a power supply of 220 V. If the current drawn by the bulb from the supply is 500 mA, the power of the bulb is :$
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Electric Power and Energy
14 $The minimum number of identical bulbs of rating 4V; 6W, that can work safely with desired brightness, when connected in series with a 240 V mains supply is :$
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Resistors in Series and Parallel
15 $12\,\Omega$
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Resistors in Series and Parallel
For Questions number 17 to 20, two statements are given — one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer to these questions from the codes (A), (B), (C) and (D) as given below.
19 $Assertion (A) : The bending of a wire in the form of a coil of several turns does not affect its electrical resistance. Reason (R) : The electrical resistance of a wire is directly proportional to its electrical resistivity.$
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Resistance and Resistivity
For Questions number 17 to 20, two statements are given — one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer to these questions from the codes (A), (B), (C) and (D) as given below.
19 $Assertion (A) : Nichrome is an alloy which is commonly used in electrical heating devices such as electric irons, toasters, etc. Reason (R) : The resistivity of nichrome is high and its resistance decreases with increase in temperature.$
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Heating Effect of Electric Current
22 (a) $Consider the following circuits : In which circuit will the power dissipated in the circuit be (I) minimum (II) maximum ? Justify your answer.$
Electric Power and Energy
22 (a) $\mathrm{R_A} : \mathrm{R_B}$
Electric Power and Energy
22 (a) $\frac{1}{5}\,\Omega$
Resistors in Series and Parallel
22 (a) $6\,\Omega$
Ohm's Law
22 (b) $4\,\Omega$
Heating Effect of Electric Current
22 (b) $4\,\Omega$
Heating Effect of Electric Current
22 (b) $Prove that if the current through a resistor is increased by 100%, then the increase in power dissipated through the resistor will be 300%.$
Electric Power and Energy
22 (b) $Two lamps, rated 100 W; 220 V and 60 W; 220 V are connected in parallel to electric main supply of 220 V. Find the current drawn by the two lamps from the supply.$
Electric Power and Energy
25 (a) $(A) State two applications of Joule’s heating in domestic electric circuit. (B) Establish the relationship between the commercial unit of electric energy and the SI unit of electric energy.$
Heating Effect of Electric Current
25 (a) $A wire of resistance R is cut into three equal parts. If these three parts are then joined in parallel, calculate the total resistance of the combination so formed.$
Resistors in Series and Parallel
25 (b) $Define electric power. When do we say that the power consumed in an electric circuit is 1 watt ?$
Electric Power and Energy
25 (b) $2\,\Omega$
Resistors in Series and Parallel
26 $How and why is an electric fuse used in an electric circuit ? Briefly describe its function.$
Heating Effect of Electric Current
26 $An electric kettle is rated 750 W; 220 V. Can this kettle be used in a circuit which has a fuse of current rating 3 A ? Give reason for your answer.$
Electric Power and Energy
26 $An electric kettle is rated 230 V; 1000 W. Calculate the resistance of its heating element when in operation.$
Electric Power and Energy
26 $An electric fuse is rated 8 A. Can it be used with an electrical appliance of rating 5 kW, 200 V ? Justify your answer.$
Electric Power and Energy
26 $40\,\Omega$
Heating Effect of Electric Current
26 $2{\cdot}0\,\Omega$
Resistors in Series and Parallel
26 $State the role of an electric fuse, used in series with an electrical appliance. Why should in an electric circuit a fuse with defined rating not be replaced by one with a larger rating?$
Heating Effect of Electric Current
27 $1{\cdot}5$
Potential Difference
27 $0{\cdot}01$
Resistance and Resistivity
32 $44 \times 10^{-6}$
Resistance and Resistivity
32 $Define the term “potential difference” between two points in an electric circuit carrying current. Name and define its S.I. unit. Also express it in terms of S.I. unit of work and charge.$
Potential Difference
32 $10\,\Omega$
Resistors in Series and Parallel
32 $35\,\Omega$
Resistance and Resistivity
32 $2\,\Omega$
Resistors in Series and Parallel
32 $\Omega$
Resistance and Resistivity
33 $(a) Write the relationship between resistivity and resistance of a cylindrical conductor of length l and area of cross-section A. Hence derive the SI unit of resistivity. (b) Why are alloys used in electrical heating devices ?$
Resistance and Resistivity
33 $(a) Explain the statement “Potential difference between two points is 1 volt”. (b) What do the symbols given below represent in an electric circuit ? Write one function of each.$
Potential Difference
Study the circuit shown in which two resistors X and Y of resistances $3\,\Omega$ and $6\,\Omega$ respectively are joined in series with a battery of 2 V.
39 (I) $Draw a circuit diagram showing the above two resistors X and Y joined in parallel with same battery and same ammeter and voltmeter.$
Resistors in Series and Parallel
As shown in the diagram, an electric circuit consisting of an ammeter, a voltmeter, 4 cells of $1{\cdot}5$ V each, a plug key with a gap XY was set up. Voltmeter and ammeter readings were recorded in the observation table for four arrangements as given below : Arrangement No. 1 – only resistor $\mathrm{R_1}$ in gap XY Arrangement No. 2 – only resistor $\mathrm{R_2}$ in gap XY Arrangement No. 3 – Resistors $\mathrm{R_1}$ and $\mathrm{R_2}$ in series in gap XY Arrangement No. 4 – Resistors $\mathrm{R_1}$ and $\mathrm{R_2}$ in parallel in gap XY Based on the observations, four V – I graphs A, B, C and D as shown in figure were drawn. Study these graphs.
39 (a) $\mathrm{R_1}$
Resistors in Series and Parallel
Study the circuit shown in which two resistors X and Y of resistances $3\,\Omega$ and $6\,\Omega$ respectively are joined in series with a battery of 2 V.
39 (II) $In which combination of resistors will the (i) potential difference across X and Y and (ii) current through X and Y, be the same ?$
Resistors in Series and Parallel
As shown in the diagram, an electric circuit consisting of an ammeter, a voltmeter, 4 cells of $1{\cdot}5$ V each, a plug key with a gap XY was set up. Voltmeter and ammeter readings were recorded in the observation table for four arrangements as given below : Arrangement No. 1 – only resistor $\mathrm{R_1}$ in gap XY Arrangement No. 2 – only resistor $\mathrm{R_2}$ in gap XY Arrangement No. 3 – Resistors $\mathrm{R_1}$ and $\mathrm{R_2}$ in series in gap XY Arrangement No. 4 – Resistors $\mathrm{R_1}$ and $\mathrm{R_2}$ in parallel in gap XY Based on the observations, four V – I graphs A, B, C and D as shown in figure were drawn. Study these graphs.
39 (b) $\mathrm{R_1}$
Resistors in Series and Parallel
Study the circuit shown in which two resistors X and Y of resistances $3\,\Omega$ and $6\,\Omega$ respectively are joined in series with a battery of 2 V.
39 (III) (a) $Find the current drawn from the battery by the series combination of the two resistors (X and Y).$
Resistors in Series and Parallel
As shown in the diagram, an electric circuit consisting of an ammeter, a voltmeter, 4 cells of $1{\cdot}5$ V each, a plug key with a gap XY was set up. Voltmeter and ammeter readings were recorded in the observation table for four arrangements as given below : Arrangement No. 1 – only resistor $\mathrm{R_1}$ in gap XY Arrangement No. 2 – only resistor $\mathrm{R_2}$ in gap XY Arrangement No. 3 – Resistors $\mathrm{R_1}$ and $\mathrm{R_2}$ in series in gap XY Arrangement No. 4 – Resistors $\mathrm{R_1}$ and $\mathrm{R_2}$ in parallel in gap XY Based on the observations, four V – I graphs A, B, C and D as shown in figure were drawn. Study these graphs.
39 (c) (i) $10\,\Omega$
Resistors in Series and Parallel
Study the circuit shown in which two resistors X and Y of resistances $3\,\Omega$ and $6\,\Omega$ respectively are joined in series with a battery of 2 V.
39 (III) (b) $Determine the equivalent resistance of the parallel combination of the two resistors (X and Y).$
Resistors in Series and Parallel
As shown in the diagram, an electric circuit consisting of an ammeter, a voltmeter, 4 cells of $1{\cdot}5$ V each, a plug key with a gap XY was set up. Voltmeter and ammeter readings were recorded in the observation table for four arrangements as given below : Arrangement No. 1 – only resistor $\mathrm{R_1}$ in gap XY Arrangement No. 2 – only resistor $\mathrm{R_2}$ in gap XY Arrangement No. 3 – Resistors $\mathrm{R_1}$ and $\mathrm{R_2}$ in series in gap XY Arrangement No. 4 – Resistors $\mathrm{R_1}$ and $\mathrm{R_2}$ in parallel in gap XY Based on the observations, four V – I graphs A, B, C and D as shown in figure were drawn. Study these graphs.
39 (c) (ii) $0{\cdot}1\,\Omega$
Resistors in Series and Parallel

Material	Resistivity ( $\Omega$ m)
A	$10^{17}$
B	$44 \times 10^{-6}$
C	$1.62 \times 10^{-8}$

2024

43 q

13 $1\,\Omega$
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Resistors in Series and Parallel
14 $20\,\Omega$
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Heating Effect of Electric Current
14 $S.I. unit of electrical resistivity is$
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Resistance and Resistivity
14 $In case of four wires of same material, the resistance will be minimum if the diameter and length of the wire respectively are$
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Resistance and Resistivity
14 $\frac{1}{5}\,\Omega$
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Resistors in Series and Parallel
14 $In the given circuit the total resistance between X and Y is :$
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Resistors in Series and Parallel
15 $10\,\Omega$
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Resistors in Series and Parallel
15 $\mathrm{R_1}$
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Ohm's Law
For Questions number 17 to 20, two statements are given — one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer to these questions from the codes (A), (B), (C) and (D) as given below.
19 $Assertion (A) : Electrons move from lower potential to higher potential in a conductor. Reason (R) : A dry cell maintains electric potential difference across the ends of a conductor.$
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Potential Difference
25 (A) $6\,\Omega$
Resistors in Series and Parallel
25 (B) $2\,\Omega$
Electric Power and Energy
25 $3\,\Omega$
Resistors in Series and Parallel
26 $0{\cdot}2$
Resistance and Resistivity
26 $An electric source can supply a charge of 500 coulomb. If the current drawn by a device is 25 mA, find the time in which the electric source will be discharged completely.$
Electric Current and Circuits
26 $An electric source can supply a charge of 750 coulomb. If the current drawn by a device is 15 mA, find the time in which the electric source will be discharged completely.$
Electric Current and Circuits
26 $State Joule’s law of heating. How is this effect useful in electric circuits where fuse is used as a safety device ?$
Heating Effect of Electric Current
26 $\mathrm{mm^2}$
Resistance and Resistivity
26 $0{\cdot}5$
Electric Current and Circuits
32 $25\,\Omega$
Electric Power and Energy
32 $Explain in brief the function of an electric fuse in a domestic circuit. An electric heater of current rating 3 kW; 220 V is to be operated in an electric circuit of rating 5 A. What is likely to happen when the heater is switched ‘ON’ ? Justify your answer with necessary calculation.$
Heating Effect of Electric Current
32 $2\,\Omega$
Resistors in Series and Parallel
33 $R_p$
Resistors in Series and Parallel
33 $List three advantages of parallel circuits in domestic wiring.$
Resistors in Series and Parallel
34 (A) $24\,\Omega$
Electric Power and Energy
34 (B) $6\,\Omega$
Resistors in Series and Parallel
36 (A) $(i) Define electric power. Express it in terms of potential difference (V) and resistance (R). (ii) An electric oven is designed to work on the mains voltage of 220 V. This oven consumes 11 units of electrical energy in 5 hours. Calculate : (a) power rating of the oven (b) current drawn by the oven (c) resistance of the oven when it is red hot$
Electric Power and Energy
36 (a) $(i) Which type of circuits — series or parallel, should be used when you have to operate different electrical gadgets in your house ? List two reasons for your answer. (ii) Find the current flowing through the following electric circuit :$
Resistors in Series and Parallel
36 (a) $1{\cdot}5$
Resistors in Series and Parallel

36 (b)

0{\cdot}5

I (Amperes)	$0{\cdot}5$	$1{\cdot}0$	$2{\cdot}0$	$3{\cdot}0$	$3{\cdot}5$
V (Volts)	$1{\cdot}5$	$3{\cdot}0$	$6{\cdot}2$	$9{\cdot}3$	$10{\cdot}8$

Ohm's Law

36 (B) $\rho$
Resistance and Resistivity
36 (b) $0{\cdot}2$
Resistance and Resistivity
When electric current flows in a purely resistive circuit electrical energy gets fully converted into heat energy. The amount of heat produced (H) in the circuit is found to be directly proportional to (i) the square of current $(I^2)$ (ii) the resistance (R) of the conductor and (iii) the time (t) for which current flows. In other words $H = I^2Rt$ . Electrical devices such an electric fuse, electric heater, electric iron etc. are all based on this effect called heating effect of electric current.
39 (a) $List two properties of heating elements.$
Heating Effect of Electric Current
In a domestic circuit five LED bulbs are arranged as shown. The source voltage is 220 V and the power rating of each bulb is marked in the circuit diagram. Based on the following circuit diagram, answer the following questions :
39 (a) $\mathrm{K_1}$
Electric Current and Circuits
Study the following circuit :
39 (a) $Find the value of total resistance between the points A and B.$
Resistors in Series and Parallel
When electric current flows in a purely resistive circuit electrical energy gets fully converted into heat energy. The amount of heat produced (H) in the circuit is found to be directly proportional to (i) the square of current $(I^2)$ (ii) the resistance (R) of the conductor and (iii) the time (t) for which current flows. In other words $H = I^2Rt$ . Electrical devices such an electric fuse, electric heater, electric iron etc. are all based on this effect called heating effect of electric current.
39 (b) $List two properties of electric fuse.$
Heating Effect of Electric Current
Study the following circuit :
39 (b) $Find the resistance between the points B and C.$
Resistors in Series and Parallel
In a domestic circuit five LED bulbs are arranged as shown. The source voltage is 220 V and the power rating of each bulb is marked in the circuit diagram. Based on the following circuit diagram, answer the following questions :
39 (b) $Find the current drawn by the bulb B when it glows.$
Electric Power and Energy
In a domestic circuit five LED bulbs are arranged as shown. The source voltage is 220 V and the power rating of each bulb is marked in the circuit diagram. Based on the following circuit diagram, answer the following questions :
39 (c) $Calculate (i) the resistance of bulb B, and (ii) total resistance of the combination of four bulbs B, C, D and E.$
Resistors in Series and Parallel
Study the following circuit :
39 (c) (i) $Calculate the current drawn from the battery, when the key is closed.$
Resistors in Series and Parallel
When electric current flows in a purely resistive circuit electrical energy gets fully converted into heat energy. The amount of heat produced (H) in the circuit is found to be directly proportional to (i) the square of current $(I^2)$ (ii) the resistance (R) of the conductor and (iii) the time (t) for which current flows. In other words $H = I^2Rt$ . Electrical devices such an electric fuse, electric heater, electric iron etc. are all based on this effect called heating effect of electric current.
39 (c) $Name the principle on which an electric fuse works. Explain how a fuse wire is capable of saving electrical appliances from getting damaged due to accidently produced high currents.$
Heating Effect of Electric Current
When electric current flows in a purely resistive circuit electrical energy gets fully converted into heat energy. The amount of heat produced (H) in the circuit is found to be directly proportional to (i) the square of current $(I^2)$ (ii) the resistance (R) of the conductor and (iii) the time (t) for which current flows. In other words $H = I^2Rt$ . Electrical devices such an electric fuse, electric heater, electric iron etc. are all based on this effect called heating effect of electric current.
39 (c) OR $The power of an electric heater is 1100 W. If the potential difference between the two terminals of the heater is 220 V, find the current flowing in the circuit. What will happen to an electric fuse of rating 5 A connected in this circuit ?$
Electric Power and Energy
In a domestic circuit five LED bulbs are arranged as shown. The source voltage is 220 V and the power rating of each bulb is marked in the circuit diagram. Based on the following circuit diagram, answer the following questions :
39 (c) OR $\mathrm{K_1}$
Resistors in Series and Parallel
Study the following circuit :
39 (c) (ii) $16\,\Omega$
Resistors in Series and Parallel

2023

25 q

13 $\mathrm{R_s}$
Tap an option to check your answer.
Resistors in Series and Parallel
13 $The expressions that relate (i) Q, I and t and (ii) Q, V and W respectively are (Here the symbols have their usual meanings) :$
Tap an option to check your answer.
Potential Difference
13 $Two LED bulbs of 12W and 6W are connected in series. If the current through 12W bulb is 0.06A the current through 6W bulb will be :$
Tap an option to check your answer.
Resistors in Series and Parallel
14 $An electric iron of 1500 W, 200 V and a flash light of 500 W, 200 V are used in homes. The rating of fuse to be used should be$
Tap an option to check your answer.
Heating Effect of Electric Current
14 $For verifying Ohm’s law, we design an electric circuit diagram in which we show the arrangement of different circuit components. We find that with respect to the resistor, the :$
Tap an option to check your answer.
Ohm's Law
15 $The resistance of a resistor is reduced to half of its initial value. If other parameters of the electrical circuit remain unaltered, the amount of heat produced in the resistor will become :$
Tap an option to check your answer.
Heating Effect of Electric Current
15 $In the following diagram, the position of the needle is shown on the scale of a voltmeter. The least count of the voltmeter and the reading shown by it respectively are :$
Tap an option to check your answer.
Potential Difference
15 $An electric kettle consumes 1 kW of electric power when operated at 220 V. The minimum rating of the fuse wire to be used for it is$
Tap an option to check your answer.
Heating Effect of Electric Current
15 $In a resistive circuit if the current is increased to two times, the percentage change in the amount of heat dissipated in the circuit would be :$
Tap an option to check your answer.
Heating Effect of Electric Current
16 $Two LED bulbs of 10W and 5W are connected in series. If the current flowing through 5W bulb is 0.005A, the current flowing through 10W bulb is :$
Tap an option to check your answer.
Resistors in Series and Parallel
16 $If the current I through a resistor is increased by 100% (at constant temperature), the increase in power dissipated will be$
Tap an option to check your answer.
Electric Power and Energy
24 $\Omega$
Resistors in Series and Parallel
24 $Let the resistance of an electrical device remain constant, while the potential difference across its two ends decreases to one fourth of its initial value. What change will occur in the current through it ? State the law which helps us in solving the above stated question.$
Ohm's Law
25 $V - I graph for two conducting wires A and B are as shown. If both wires are of the same length and same diameter, which of the two is made of a material of high resistivity ? Give reasons to justify your answer.$
Resistance and Resistivity
34 $10\,\Omega$
Resistors in Series and Parallel
35 $8{\cdot}00$
Electric Power and Energy
36 (a) $(i) What is meant by resistance of a conductor ? Define its SI unit. (ii) List two factors on which the resistance of a rectangular conductor depends. (iii) How will the resistance of a wire be affected if its (1) length is doubled, and (2) radius is also doubled ? Give justification for your answer.$
Resistance and Resistivity
36 (b) $In an electric circuit three bulbs of 100 W each are connected in series to a source. In another circuit set of three bulbs of the same wattage are connected in parallel to the same source. (i) Will the bulb in the two circuits glow with the same brightness ? Justify your answer. (ii) Now, let one bulb in both the circuits get fused. Will the rest of the bulbs continue to glow in each circuit ? Give reason for your answer.$
Resistors in Series and Parallel
36 $(a) State Ohm’s Law. (b) Name and define the physical quantity determined by the slope of V - I curve given in the diagram. Use this graph to find the value of this physical quantity in SI units. (c) Establish the relationship between 1 kWh and 1 joule.$
Ohm's Law
36 $(a) An electric iron consumes energy at a rate of 880 W when heating is at the maximum rate and 330 W when the heating is at the minimum. If the source voltage is 220 V, calculate the current and resistance in each case. (b) What is heating effect of electric current ? (c) Find an expression for the amount of heat produced when a current passes through a resistor for some time.$
Electric Power and Energy
36 $(i) How is electric current related to the potential difference across the terminals of a conductor ? Draw a labelled circuit diagram to verify this relationship. (ii) Why should an ammeter have low resistance ? (iii) Two V - I graphs A and B for series and parallel combinations of two resistors are as shown. Giving reason state which graph shows (a) series, (b) parallel combination of the resistors.$
Ohm's Law
Consider the following electrical circuit diagram in which nine identical resistors of $3\,\Omega$ each are connected as shown. If the reading of the ammeter $\mathrm{A_1}$ is 1 ampere, answer the following questions :
39 (a) $\mathrm{A_1}$
Resistors in Series and Parallel
Consider the following electrical circuit diagram in which nine identical resistors of $3\,\Omega$ each are connected as shown. If the reading of the ammeter $\mathrm{A_1}$ is 1 ampere, answer the following questions :
39 (b) $\mathrm{A_2}$
Resistors in Series and Parallel
Consider the following electrical circuit diagram in which nine identical resistors of $3\,\Omega$ each are connected as shown. If the reading of the ammeter $\mathrm{A_1}$ is 1 ampere, answer the following questions :
39 (c) $\mathrm{V_1}$
Resistors in Series and Parallel
Consider the following electrical circuit diagram in which nine identical resistors of $3\,\Omega$ each are connected as shown. If the reading of the ammeter $\mathrm{A_1}$ is 1 ampere, answer the following questions :
39 (c) OR $Find the total resistance of the circuit.$
Resistors in Series and Parallel

2022

15 q

4 (a) $An electric heater rated 1100 W operates at 220 V. Calculate (i) its resistance, and (ii) the current drawn by it.$
Electric Power and Energy
4 (b) $Calculate the equivalent resistance of the following electric circuit :$
Resistors in Series and Parallel
11 $\mathrm{R_1}$
Resistors in Series and Parallel
11 $(a) State Ohm’s Law. Represent it mathematically. (b) Define 1 ohm. (c) What is the resistance of a conductor through which a current of 0.5 A flows when a potential difference of 2 V is applied across its ends ?$
Ohm's Law
12 (a) $10\,\Omega$
Resistance and Resistivity
12 $(a) A student wants to use an electric heater, an electric bulb and an electric fan simultaneously. How should these gadgets be connected with the mains ? Justify your answer giving three reasons. (b) What is an electric fuse ? How is it connected in a circuit ?$
Resistors in Series and Parallel
12 (a) $(i) Define Electric Power and write its SI unit. (ii) Two bulbs rated 100 W; 220 V and 60 W; 220 V are connected in parallel to an electric mains of 220 V. Find the current drawn by the bulbs from the mains.$
Electric Power and Energy
13 $An electric motor rated 1100 W is connected to 220 V mains. Find : (i) The current drawn from the mains, (ii) Electric energy consumed if the motor is used for 5 hours daily for 6 days. (iii) Total cost of energy consumed if the rate of one unit is ₹ 5.$
Electric Power and Energy
12 (b) $(a) What is the meaning of electric power of an electrical device ? Write its SI unit. (b) An electric kettle of 2kW is used for 2h. Calculate the energy consumed in (i) kilowatt hour and (ii) joules.$
Electric Power and Energy
12 (b) $5\,\Omega$
Heating Effect of Electric Current
13 OR $\Omega$
Resistors in Series and Parallel
Study the following electric circuit in which the resistors are arranged in three arms A, B and C :
14 (a) $Find the equivalent resistance of arm A.$
Resistors in Series and Parallel
Study the following electric circuit in which the resistors are arranged in three arms A, B and C :
14 (b) $Calculate the equivalent resistance of the parallel combination of the arms B and C.$
Resistors in Series and Parallel
Study the following electric circuit in which the resistors are arranged in three arms A, B and C :
14 (c) (i) $Determine the current that flows through the ammeter.$
Resistors in Series and Parallel
Study the following electric circuit in which the resistors are arranged in three arms A, B and C :
14 (c) (ii) $Determine the current that flows in the ammeter when the arm B is withdrawn from the circuit.$
Resistors in Series and Parallel

The 10 board questions to practise first

The questions and kinds of question the board asked most often come first. Each one says how often and when.

Question 1
This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2026 See all 5 of this type
34 (b) $An electric heater is rated 220 V; 11 A. Calculate the power consumed if the heater is operated at 200 V.$
Question 2
This type asked 4 times: 2022, 2023, 2024, 2026. This one: 2026 See all 4 of this type
34 $(a) State the law which gives the relation between the electric current flowing through a given conductor and the potential difference applied across it. (b) Draw V-I graph for a given conductor as per the law stated in above question (a).$
Question 3
This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026 See all 4 of this type
39 (B) $4\,\Omega$
Question 4
This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026 See all 4 of this type
39 (b) $8\,\Omega$
Question 5
This type asked 4 times: 2022, 2024, 2025, 2026. This one: 2026 See all 4 of this type
39 (a) $3\,\Omega$
Question 6
This type asked 4 times: 2022, 2023, 2024, 2025. This one: 2025 See all 4 of this type
22 (b) $4\,\Omega$
Question 7 (case study, 4 parts)
This type asked 4 times: 2022, 2023, 2024, 2025. This one: 2025 See all 4 of this type
Study the circuit shown in which two resistors X and Y of resistances $3\,\Omega$ and $6\,\Omega$ respectively are joined in series with a battery of 2 V.
39 (I) $Draw a circuit diagram showing the above two resistors X and Y joined in parallel with same battery and same ammeter and voltmeter.$
39 (II) $In which combination of resistors will the (i) potential difference across X and Y and (ii) current through X and Y, be the same ?$
39 (III) (a) $Find the current drawn from the battery by the series combination of the two resistors (X and Y).$
39 (III) (b) $Determine the equivalent resistance of the parallel combination of the two resistors (X and Y).$
Question 8
Asked 3 times: 2022*, 2025*, 2026 (* = numbers or wording changed that year) See all 3 times it was asked
34 (a) $7\,\Omega$
Question 9
Asked 3 times: 2024*, 2025*, 2026 (* = numbers or wording changed that year) See all 3 times it was asked
33 (A) $A fuse in electric circuit is rated 4 A. Can it be used with an electric heater of rating 2 kW, 200 V ? Explain your answer.$
Question 10
Asked 3 times: 2024*, 2025*, 2026 (* = numbers or wording changed that year) See all 3 times it was asked
34 $(a) Define volt, the unit of potential difference. (b) Calculate the work done required to move an electron between two points A and B located at a potential difference of 100 V in an electric field.$

Quick revision

7 most-asked questions · 12 key points · 9 formulas · 3 derivations · 5 diagrams

Checked against NCERT Science (CBSE Class 10), Chapter 11.

Most asked in board papers

1
Electric power and energy: $P = VI = I^2R = \frac{V^2}{R}$ , ratings of lamps and heaters, cost in kWh, lamps in series and parallel
Asked 5 times: 2026, 2025, 2024, 2023, 2022
2
Circuit numericals: current and potential difference in each resistor, circuit diagrams, and why domestic appliances are joined in parallel
Asked 5 times: 2026, 2025, 2024, 2023, 2022 · 2 marks
3
Equivalent resistance: series and parallel formulas (derive), arranging resistors for a given value, maximum and minimum resistance
Asked 5 times: 2026, 2025, 2024, 2023, 2022
4
Heating effect: Joule's law, heater and bulb filament, why fuse and its rating
Asked 5 times: 2026, 2025, 2024, 2023, 2022 · 2 marks
5
Resistance and resistivity: factors, $R = \rho\frac{l}{A}$ , stretched or thicker wire, why alloys are used for heating
Asked 5 times: 2026, 2025, 2024, 2023, 2022
6
Ohm's law: statement, V-I graph and its slope, circuit symbols, ammeter in series and voltmeter in parallel
Asked 4 times: 2026, 2024, 2023, 2022
7
Charge, current and potential difference: define 1 volt and 1 ampere, $Q = It$ , $W = VQ$
Asked 4 times: 2026, 2025, 2024, 2023

Must-know points

Electric current: The rate of flow of electric charge: $I = \frac{Q}{t}$ . One ampere is the flow of one coulomb of charge per second. By convention current flows opposite to the flow of electrons. 1 C is the charge of about $6 \times 10^{18}$ electrons; an electron carries $1.6 \times 10^{-19}$ C. An ammeter is joined in series.
Potential difference: The work done to move a unit charge from one point to the other: $V = \frac{W}{Q}$ . 1 volt: when 1 joule of work is done to move 1 coulomb of charge between the two points. Electrons move from lower to higher potential. A voltmeter is joined in parallel.
Ohm's law: The potential difference across the ends of a resistor is directly proportional to the current through it, provided its temperature remains the same: $V = IR$ . The V-I graph is a straight line through the origin; its slope gives the resistance. 1 ohm: a current of 1 A flows when the potential difference is 1 V.
Factors affecting resistance; resistivity: Resistance depends directly on length, inversely on area of cross-section, and on the material (and temperature). $R = \rho\frac{l}{A}$ ; $\rho$ , the resistivity, is the resistance of a wire of unit length and unit area; its SI unit is ohm metre ( $\Omega$ m). It depends only on the material, not on the shape.
Alloys and conductors: Metals and alloys have low resistivity; insulators very high. An alloy has a higher resistivity than its constituent metals and does not oxidise (burn) readily at high temperatures, so nichrome is used in heating devices. Copper and aluminium are used for transmission lines; tungsten for bulb filaments.
Resistors in series: The same current flows through each resistor. The total potential difference equals the sum of the potential differences across each. The equivalent resistance is the sum: $R_s = R_1 + R_2 + R_3$ , larger than the largest.
Resistors in parallel: The same potential difference is across each resistor. The total current equals the sum of the separate currents. The reciprocal of the equivalent resistance equals the sum of the reciprocals: $R_p$ is smaller than the smallest resistor.
Why domestic wiring is parallel: In series, one failed bulb breaks the whole circuit, and all devices share one current though they need different currents. In parallel each device gets the full voltage and its own current, can be switched on and off separately, and the total resistance is less.
Heating effect: Joule's law: Heat produced in a resistor is directly proportional to the square of the current, to the resistance, and to the time for which the current flows: $H = I^2Rt$ . The source's energy is spent entirely as heat in a purely resistive circuit.
Uses of the heating effect: Electric iron, toaster, oven, kettle and heater. Electric bulb: the filament of tungsten (melting point 3380 °C) glows; the bulb is filled with inactive nitrogen and argon to prolong the filament's life. Electric fuse.
Electric fuse: A wire of a metal or alloy of suitable melting point, placed in series with the device. If a current larger than its rating flows, the wire heats up, melts and breaks the circuit, protecting the device. Domestic fuses are rated 1 A, 2 A, 3 A, 5 A, 10 A: a 1 kW, 220 V iron draws 4.54 A, so a 5 A fuse.
Electric power and energy: Power is the rate at which electric energy is consumed: $P = VI$ . SI unit watt: 1 W = 1 V × 1 A. Commercial unit of energy: kilowatt hour (kW h), the 'unit': $1\text{ kW h} = 3.6 \times 10^6$ J.

Formulas

Current and charge

\begin{gathered}I = \frac{Q}{t} \\ Q = ne \\ e = 1.6 \times 10^{-19}\text{ C}\end{gathered}

Potential difference

V = \frac{W}{Q}

Ohm's law

V = IR

Resistance and resistivity

\begin{gathered}R = \rho\,\frac{l}{A} \\ A = \pi r^2 \\ \rho = \frac{RA}{l}\end{gathered}

Series

R_s = R_1 + R_2 + R_3

Parallel

\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}

Heat produced (Joule's law)

H = VIt = I^2Rt = \frac{V^2}{R}\,t

Electric power

P = VI = I^2R = \frac{V^2}{R}

Electric energy

\begin{gathered}E = Pt \\ 1\text{ kW h} = 1000\text{ W} \times 3600\text{ s} = 3.6 \times 10^6\text{ J}\end{gathered}

Derivations

Try each one first, then open its outline.

Derive the equivalent resistance of three resistors in series

The same current I flows through $R_1$ , $R_2$ , $R_3$ ; the total potential difference $V = V_1 + V_2 + V_3$ .
By Ohm's law $V_1 = IR_1$ , $V_2 = IR_2$ , $V_3 = IR_3$ , and for the combination $V = IR_s$ .
So $IR_s = IR_1 + IR_2 + IR_3$ , giving $R_s = R_1 + R_2 + R_3$ .

Derive the equivalent resistance of three resistors in parallel

The same potential difference V is across each; the total current $I = I_1 + I_2 + I_3$ .
By Ohm's law $I_1 = \frac{V}{R_1}$ , $I_2 = \frac{V}{R_2}$ , $I_3 = \frac{V}{R_3}$ , and $I = \frac{V}{R_p}$ .
So $\frac{V}{R_p} = \frac{V}{R_1} + \frac{V}{R_2} + \frac{V}{R_3}$ , giving $\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$ .

Establish Joule's law of heating,

H = I^2Rt

Charge Q moved through potential difference V does work $W = VQ$ ; in time t, $Q = It$ .
So the energy supplied, $H = VIt$ , is all turned into heat in a resistor.
With $V = IR$ : $H = I^2Rt$ . Power $P = \frac{H}{t} = VI = I^2R$ .

Diagrams to practise

Circuit for studying Ohm's law (Figure 11.2): label cells (battery) · plug key · ammeter in series · nichrome wire XY · voltmeter in parallel across XY · rheostat
V-I graph for a nichrome wire (Figure 11.3): label I on x-axis, V on y-axis · straight line through the origin · slope V/I = R · units on both axes
Resistors in series (Figure 11.6): label R₁, R₂, R₃ end to end · battery and plug key · one ammeter anywhere in the loop · voltmeter across the combination
Resistors in parallel (Figure 11.7): label R₁, R₂, R₃ between the same two points X and Y · ammeter in the main line · voltmeter across XY · battery and plug key
Circuit symbols (Table 11.1): label cell and battery · plug key open and closed · wire joint and wires crossing · bulb, resistor, rheostat · ammeter, voltmeter

Mistakes that cost marks

Ammeter and voltmeter the wrong way

Ammeter in series (low resistance); voltmeter in parallel across the part being measured (high resistance).

Adding resistances in parallel

In parallel add the reciprocals, then invert: 2 Ω, 3 Ω, 6 Ω give

\frac{1}{R_p} = \frac{1}{2} + \frac{1}{3} + \frac{1}{6} = 1

, so

R_p = 1

Ω; in series 11 Ω.

Stretched or cut wire

Stretching a wire to 3 times its length makes its area one-third, so R becomes 9 times. Cutting a wire of resistance R into three equal parts and joining them in parallel gives

\frac{R}{9}

. Resistivity does not change.

Diameter used as radius

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

A = \pi r^2

with r in metres: 0.01 cm =

1 \times 10^{-4}

m, and

1\text{ mm}^2 = 10^{-6}\text{ m}^2

. Halving the diameter makes R four times.

Wrong power formula for the case

Same current (series): use

P = I^2R

, so the larger resistor (lower-wattage lamp) glows brighter. Same voltage (parallel): use

P = \frac{V^2}{R}

. From a rating,

R = \frac{V^2}{P}

: 220 V, 11 W gives 4400 Ω. Doubling the current makes the power four times.

Joules and kilowatt hours mixed

Energy in kW h = power in kW × time in hours. Convert to joules with

1\text{ kW h} = 3.6 \times 10^6

11.1 Electric Current and Circuit

Solved Examples

Questions

11.2 Electric Potential and Potential Difference

Solved Examples

Questions

11.4-11.5 Ohm's Law and the Factors on which Resistance Depends

Solved Examples

Questions

11.6.1 Resistors in Series

Solved Examples

Questions

11.6.2 Resistors in Parallel

Solved Examples

Questions

11.7 Heating Effect of Electric Current

Solved Examples

Questions

11.8 Electric Power

Solved Examples

Questions

Exercises

What the board has asked from this chapter

2026

2025

2024

2023

2022

The 10 board questions to practise first

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7 (case study, 4 parts)

Question 8

Question 9

Question 10

Most asked in board papers

Must-know points

Formulas

Derivations

Diagrams to practise

Mistakes that cost marks