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 gives the way $I$ changes with time $t$. When the current is in the positive direction, its magnitude is $2I_0$; when it is in the negative direction, its magnitude is $I_0$. The period of the current variation is $T$.
(a)

Determine expressions, in terms of $I_0$ and $R$, for the power $P$ dissipated in the resistor at the times when:

(a(i))[1]

the current is directed in the negative direction.

(a(ii))[1]

the current is directed in the positive direction.

(b)[3]

On Fig. 7.3, sketch the variation of $P$ with $t$ between $t = 0$ and $t = 2.0T$. Add an appropriate scale to the power axis.

(c(i))[1]

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

(c(ii))[2]

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

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