Physics 9702 · AS & A Level · Kirchhoff's laws

Kirchhoff's laws — practice question

(a)[2]

State Kirchhoff’s second law.

(b)

Two batteries, each with electromotive force (e.m.f.) $6.0\,\text{V}$ and negligible internal resistance, are arranged in series with three resistors, as shown in Fig. 5.1. Resistor X has resistance $4.0\,\Omega$ and resistor Y has resistance $1.5\,\Omega$.

(b(i)1)[1]

The resistance $R$ of the variable resistor is adjusted until the voltmeter in the circuit shows zero. Calculate the current $I$ in the circuit.

(b(i)2)[2]

Calculate the resistance $R$.

(b(ii))[2]

Resistors X and Y are wires made from the same material. The diameter of the wire of X is twice the diameter of the wire of Y. Determine the ratio average drift speed of free electrons in X : average drift speed of free electrons in Y.

(b(iii))[3]

The resistance $R$ of the variable resistor is now increased. State and explain the effect of the increase in $R$ on the power transformed by each of the batteries.

(ii)[2]

Resistors $X$ and $Y$ are wires made from the same material. The diameter of the wire of $X$ is twice the diameter of the wire of $Y$. Determine the ratio $\dfrac{\text{average drift speed of free electrons in } X}{\text{average drift speed of free electrons in } Y}$.

(iii)[3]

The resistance $R$ of the variable resistor is now increased. State and explain the effect of the increase in $R$ on the power transformed by each of the batteries.

Worked solution & mark scheme

This 15-mark question has a full step-by-step worked solution and mark scheme. One marking point: the sum of the e.m.f.s is equal to the sum of the p.d.s

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