Question

An alternating voltage E = E₀ sin ωt is applied to a circuit containing a resistor R connected in series with a black box. The current in the circuit is found to be I = I₀ sin (ωt + \(\frac{\pi}{4}\)).

(i) State whether the element in the black box is a capacitor or inductor.

(ii) Draw the corresponding phasor diagram and find the impedance in terms of R.

Answer 1

(i) Here we find that the current leads the voltage by a phase \(\frac{\pi}{4}\), so the element in the black box is a capacitor.

(ii) Phasor diagram is shown in fig.