CAIE A-Level Physics 10.2 Kirchhoff's Laws

Practise applying Kirchhoff’s laws, deriving series and parallel resistance formulae and solving multi-loop currents, potential differences and resistances.

Exam points

apply Kirchhoff’s first and second laws as conservation of charge and energy
derive and use equivalent resistance formulae for series and parallel networks
solve multi-loop circuit problems for currents, potential differences and resistances using consistent signs and junction/loop equations

Covered syllabus points

10.2.1—Kirchhoff’s first law and understand that it is a consequence of 10.2.2—Kirchhoff’s second law and understand that it is a consequence of 10.2.3—Kirchhoff’s laws, a formula for the combined resistance of two or more 10.2.4—The formula for the combined resistance of two or more resistors in series 10.2.5—Kirchhoff’s laws, a formula for the combined resistance of two or more 10.2.6—The formula for the combined resistance of two or more resistors in parallel 10.2.7—Kirchhoff’s laws to solve simple circuit problems

[Maximum number: 5]

(a)

State Kirchhoff's first law.

[ 1 ]

(b)

A cell with internal resistance r is connected to two resistors of resistances $R_{1}$ and $R_{2}$ as shown in Fig. 6.1.

Fig. 6.1

The potential differences (p.d.s) across $R_{1}$ and $R_{2}$ are $V_{1}$ and $V_{2}$ respectively.
The terminal p.d. across the cell is V.
The current in the circuit is I.

Use Kirchhoff's laws to show that the total resistance $R_{\mathrm{T}}$ of the external circuit is given by

R_{\mathrm{T}}=R_{1}+R_{2} .

[ 2 ]

(by Kirchhoff's second law) $V=V_{1}+V_{2}$

B1

so $I R_{\mathrm{T}}=I R_{1}+I R_{2}($ and cancelling I gives $) R_{\mathrm{T}}=R_{1}+R_{2}$

or

$V / I=V_{1} / I+V_{2} / I$ (and substituting R gives) $R_{\mathrm{T}}=R_{1}+R_{2}$

B1

(c)

A resistor of resistance $R_{3}$ is added to the circuit in Fig. 6.1, so that the circuit is as shown in Fig. 6.2.

Fig. 6.2

State and explain the effect, if any, of this change on:

[ 2 ]

(i)

the current in the cell

[ 2 ]

[Maximum number: 2]

State Kirchhoff's second law.

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Covered syllabus points

10.2 Kirchhoff’s laws question 1

Question (a)

Question (b)

Question (c)

Question (i)

10.2 Kirchhoff’s laws question 2