Physics 9702 · AS & A Level · Characteristics of alternating currents

Characteristics of alternating currents — practice question

A time-varying current $I$ flows through a resistor of resistance $R$ in the circuit shown in Fig. 7.1. Fig. 7.2 plots how $I$ changes with time $t$. The current has magnitude $2I_0$ while it is in the positive direction, and magnitude $I_0$ while it is in the negative direction. The period of the current variation is $T$.
(a(i))[1]

Determine expressions, in terms of $I_0$ and $R$, for the power $P$ dissipated in the resistor during the intervals when the current is negative.

(a(ii))[1]

Determine expressions, in terms of $I_0$ and $R$, for the power $P$ dissipated in the resistor during the intervals when the current is positive.

(b)[3]

On Fig. 7.3, sketch the variation of $P$ with $t$ from $t = 0$ to $t = 2.0T$. Mark the power axis with a suitable scale.

(c(i))[1]

Use your answer in (b) to determine an expression, in terms of $I_0$ and $R$, for the mean power $\langle P \rangle$ in the resistor.

(c(ii))[2]

Use your answer in (b) to determine an expression, in terms of $I_0$ and $R$, for the root-mean-square (r.m.s.) current $I_{\text{r.m.s.}}$ in the resistor.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: $P = I_0^2 R$

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