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

Kirchhoff's laws — practice question

A battery with electromotive force (e.m.f.) $12\,\text{V}$ and internal resistance $r$ is joined in series to two resistors, each of fixed resistance $X$, as shown in Fig. 5.1. The current $I_1$ delivered by the battery is $1.2\,\text{A}$. The same battery is then connected to the same two resistors in parallel, as shown in Fig. 5.2. The current $I_2$ delivered by the battery is $3.0\,\text{A}$.
(a(i))[2]

Demonstrate that the combined resistance of the two resistors, each of resistance $X$, is four times larger in Fig. 5.1 than in Fig. 5.2.

(a(ii))[2]

Explain why $I_2$ is not four times as large as $I_1$.

(a(iii)-1)[1]

Using Kirchhoff’s second law, state equations, in terms of e.m.f., current, $X$ and $r$, for the circuit of Fig. 5.1.

(a(iii)-2)[1]

Using Kirchhoff’s second law, state equations, in terms of e.m.f., current, $X$ and $r$, for the circuit of Fig. 5.2.

(a(iv))[1]

Use the equations in (a)(iii) to calculate the resistance $X$.

(b)[2]

Calculate the ratio $$\frac{\text{power dissipated in one resistor of resistance }X\text{ in Fig. 5.1}}{\text{power dissipated in one resistor of resistance }X\text{ in Fig. 5.2}}.$$

(c)[2]

In Fig. 5.1 and Fig. 5.2 the resistors are replaced with identical $12\,\text{V}$ filament lamps. Explain why the resistance of each lamp when it is in series is not the same as the resistance of each lamp when it is in parallel.

(a(iii))[2]

Using Kirchhoff’s second law, state equations, in terms of e.m.f., current, $X$ and $r$, for 1. the circuit of Fig. 5.1, 2. the circuit of Fig. 5.2.

Worked solution & mark scheme

This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: Equivalent resistance equals $2X$ for series connections or $\dfrac{X}{2}$ for parallel connections

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI