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

Characteristics of alternating currents — practice question

The output from a power supply can be written as $V = 9.0 \sin 20t$, with $V$ denoting potential difference in volts and $t$ representing time in seconds.
(a(i))[1]

Find the root-mean-square (r.m.s.) voltage, $V_{\text{r.m.s.}}$.

(a(ii))[2]

Find the period $T$.

(b)[1]

The changes in output potential difference $V$ with time $t$ for two different power supplies are shown in Fig. 9.1 and Fig. 9.2. The graphs use the same scale. State and explain whether the power dissipated in a $1.0\,\Omega$ resistor connected to each power supply is the same.

(c(i))[3]

In part (a), the power supply is linked to a transformer. The transformer’s input power is $80\,\text{W}$. A resistor is connected to the secondary coil. The r.m.s. voltage across the resistor is $120\,\text{V}$. The r.m.s. current in the secondary coil is $0.64\,\text{A}$. Calculate the efficiency of the transformer.

(c(ii))[1]

State one reason why the transformer is not $100\%$ efficient.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Hence, $\frac{9.0}{\sqrt{2}} = 6.4\,\text{V}$.

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