In an AC circuit containing a single pure element, the variations of voltage V and current I with time t are observed. At t = 0 , the voltage is at its positive maximum value V₀ , whereas the current is zero and is increasing in the positive direction. If the peak value of the current is I₀ , identify the circuit element and the correct expression for its reactance.

Step-by-step solution

From the given description, the voltage is at its positive maximum at t = 0 , which corresponds to a cosine function: V = V₀ t = V₀ ( t + 2 ) . The current is zero at t = 0 and increasing positively, which corresponds to a sine function: I = I₀ t . Comparing the phases, the voltage leads the current by a phase angle of 2 ( 90^ ). This is the characteristic of a purely inductive circuit. The reactance of any pure circuit element is defined as the ratio of the peak voltage to the peak current, so X_L = V₀ I₀ . Answer