Question

31.3 forced oscillations of three simple circuits
in an ac circuit containing a purely inductive load, the current in the inductor is — relative to the voltage across the inductor.
o leading by 1/4 of a cycle
o lagging by less than 1/4 of a cycle
o in phase
o lagging by 1/4 of a cycle
o leading by less than 1/4 of a cycle

Explanation:

In an AC circuit with a purely inductive load, the voltage across the inductor leads the current by \(90^{\circ}\) (or \(\frac{1}{4}\) of a cycle). This is a fundamental property of inductors in AC circuits. The relationship is derived from the inductor's voltage - current equation \(v = L\frac{di}{dt}\). When analyzing the sinusoidal steady - state (AC) behavior, using phasor analysis, the impedance of an inductor \(Z = j\omega L\). The phase angle of the impedance is \(90^{\circ}\), which means the voltage (phasor \(V = ZI\)) leads the current (phasor \(I\)) by \(90^{\circ}\) (or \(\frac{1}{4}\) of a cycle since a full cycle is \(360^{\circ}\)).

Answer:

lagging by \(1/4\) of a cycle