$A$ device $'X'$ is connected to an a.c. source. The variation of voltage,current,and power in one complete cycle is shown in the figure.
$(a)$ Which curve shows power consumption over a full cycle?
$(b)$ What is the average power consumption over a cycle?
$(c)$ Identify the device $'X'$.

(A) We know that power $P = VI$. The curve of power will have a maximum amplitude equal to the product of the amplitudes of the voltage and current curves. Therefore,the curve is represented by $A$.
$(b)$ As shown by the shaded area in the diagram,the full cycle of the graph consists of one positive and one negative symmetrical area.
Hence,the average power over a cycle is zero.
$(c)$ Since the average power is zero,the device $'X'$ must be a pure inductor $(L)$,a pure capacitor $(C)$,or a series combination of $L$ and $C$ (i.e.,a purely reactive circuit).