10.2 Kirchhoff’s Laws | CIE AS Physics Topic Questions 2025

1a

3 marks

Three resistors of resistances R₁, R₂ and R₃ are connected as shown in Fig. 1.1.

Fig 1.1

The potential difference across the resistors are V₁, V₂ and V₃. The current in the combination of resistors is I.

Show that the total resistance R of the combination is given by the equation.

R = R_{1} + R_{2} + R_{3}

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1b

3 marks

Three resistors are placed in a circuit with a cell of 10 V and negligible internal resistance and two switches S₁ and S₂. This is shown in Fig 1.1.

Fig 1.1

Complete table 1.1.

Table 1.1

Position of switches
S₁	S₂	Total resistance / kΩ
open	closed
closed	open
closed	closed

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1c

2 marks

The cell has an e .m .f of 10 V and negligible internal resistance.

Calculate the current from the cell when

(i)

switch S₁ is closed,

[1]

(ii)

both S₁ and S₂ are closed.

[1]

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1d

3 marks

Using your answers in part (c), determine the current from the cell if just switch S₂ is closed.

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1a

4 marks

A circuit containing a junction P has two power supplies with e.m.f 6.0 V and 2.0 V and two resistors with resistance 30 Ω and 10 Ω is shown in Fig. 1.1.

10-2-q1a-h-sq-cie-ial-physics

Fig. 1.1

Draw on the diagram to label the currents in each branch of the circuit and obtain an expression for the current at P.

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1b

4 marks

Determine the values of the currents at P for the circuit in part a).

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1c

2 marks

A combination of identical resistors each with resistance R has a total resistance of 250 Ω as shown in Fig. 1.2.

sl-sq-5-2-hard-q1a-qun-series-resistors

Fig. 1.2

Show, without the use of a calculator, how to find the value of resistance of each resistor and hence determine the value of R.

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1d

4 marks

A student wishes to determine the resistance for three different resistors. They connect the resistors in a ‘T’ arrangement and change the position of the power source and the voltmeter, as shown in Fig. 1.1, to obtain two sets of results, as shown in Table 1.1. The power supply in Circuit 1 causes a current of 0.50 A in one branch of a circuit.

Fig. 1.1

Table 1.1

Circuit	Voltage supplied by power source /V	Reading on voltmeter /V
1	8.0	5.0
2	10	4.0

Calculate the resistance of resistors $R_{1}$ , $R_{2}$ and $R_{3}$ .

You may assume the voltmeter has an infinitely high resistance.

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1a

2 marks

Three resistors of resistances R₁, R₂ and R₃ are connected as shown in Fig. 1.1.

The currents in the resistors are I₁, I₂ and I₃. The total current in the combination of resistors is I and the potential difference across the combination is V.

Show that the total resistance R of the combination is given by the equation

$\frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}$

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1b

10 marks

A battery of electromotive force (e.m.f.) 6.0 V and internal resistance r is connected to an external resistor of resistance 12 Ω and a thermistor X, as shown in Fig. 1.2.

q6b-paper-2-specimen-2022-cie-ial-physics

Fig. 1.2

(i)

By considering energy, explain why the potential difference across the terminals of the battery is less than the e.m.f.

[1]

(ii)

A charge of 2.5 kC passes through the battery.

Calculate:

• the total energy transferred by the battery

energy = ............................................................ J

• the number of electrons that pass through the battery.

number = .......................................[3]

(iii)

The combined resistance of the external resistor and thermistor X connected in parallel is 4.8 Ω.

Calculate the resistance of X.

resistance = ........................................ Ω [1]

(iv)

Use your answer in (b)(iii) to determine the ratio

\frac{power dissipated in thermistor X}{power dissipated in 12 Ω resistor}

ratio = .................................. [2]

(v)

The temperature of thermistor X is now decreased.

State and explain the effect, if any, of this temperature change on the total power produced by the battery.

[3]

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2a

1 mark

A student investigates the potential difference in a circuit. The circuit is set up as shown in Fig. 2.1.

q2-paper-5-specimen-2022-cie-ial-physics

Fig. 2.1

Two resistors P and Q are connected in series to a power supply of electromotive force (e.m.f.) E and negligible internal resistance. Resistor P has resistance P.

The potential difference V across resistor P is measured. The experiment is repeated for different values of P.

It is suggested that V and P are related by the equation

$V = (\frac{P}{P + Q}) E$

where Q is the resistance of resistor Q. The value of Q is kept constant.

A graph is plotted of $\frac{1}{V}$ on the y-axis against $\frac{1}{P}$ on the x-axis.

Determine expressions for the gradient and the y-intercept.

gradient = ............................................
y-intercept = .......................................

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2b

2 marks

Values of P, V and $\frac{1}{V}$ are given in Table 2.1.

Table 2.1

P / Ω	V / V	$\frac{1}{P}$ / 10^–3 Ω^–1	$\frac{1}{V}$ / V^–1
250	0.66		1.52
330	0.86		1.16
470	1.15		0.870
560	1.30		0.769
680	1.49		0.671
840	1.64		0.610

Each value of P has an uncertainty of ±10%.

Calculate and record values of $\frac{1}{P}$ / 10^–3 Ω^–1 in Table 2.1.

Include the absolute uncertainties in $\frac{1}{P}$ .

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2c

8 marks

(i)

Plot a graph of

\frac{1}{V}

/ V^–1 against

\frac{1}{P}

/ 10^–3 Ω^–1.

Include error bars for

\frac{1}{P}

.

[2]

(ii)

Draw the straight line of best fit and a worst acceptable straight line on your graph. Label both lines.

[2]

(iii)

Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer.

gradient = ......................................... [2]

(iv)

Determine the y-intercept of the line of best fit. Include the absolute uncertainty in your answer.

y-intercept = ......................................... [2]

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2d

4 marks

(i)

Using your answers to (a), (c)(iii) and (c)(iv), determine the values of E and Q. Include appropriate units.

E = ..............................................
Q = .............................................
[2]

(ii)

Determine the percentage uncertainty in E.

percentage uncertainty in E = ......................................... % [1]

(iii)

Determine the absolute uncertainty in Q.

absolute uncertainty in Q = ........................................ [1]

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Kirchhoff’s Laws (CIE AS Physics)

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