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The output of an AC generator is given by \(E=E_m\sin(\omega t-\pi/4)\) and current is given by \(i=i_m\sin(\omega t-3\pi/4)\). The circuit contains a single element other than the generator. It is:

1. a capacitor.
2. a resistor.
3. an inductor.
4. not possible to decide due to lack of information.

Correct answer: an inductor.

Solution

The voltage phase is \(-\pi/4\) and the current phase is \(-3\pi/4\), so current lags voltage by \(\pi/2\). In a pure inductive circuit, current lags voltage by 90°, hence the element is an inductor.

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