Concept:In a purely capacitive AC circuit, the alternating current leads the alternating voltage across the capacitor by a phase angle of \(90^\circ\) (\(\frac{\pi}{2}\text{ rad}\)).
Formula / Reaction:$$q = C V \implies I = \frac{\Delta q}{\Delta t}$$
Solution:- When an alternating voltage \(V = V_0 \sin(\omega t)\) is applied across a capacitor, the instantaneous current is \(I = I_0 \cos(\omega t) = I_0 \sin\left(\omega t + \frac{\pi}{2}\right)\).
- The rate of change of charge (and hence current) reaches its maximum when the voltage is zero.
- Therefore, current leads the alternating voltage by a phase difference of \(90^\circ\) (or \(\frac{\pi}{2}\text{ rad}\)).
Why other options are incorrect:Current lagging behind voltage by \(90^\circ\) occurs in purely inductive circuits; current in-phase with voltage occurs in purely resistive circuits; a \(45^\circ\) phase angle occurs only in series \(RC\) circuits where \(R = X_C\).
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