Concept:In a pure capacitor, alternating current is proportional to the rate of change of voltage across its plates: \(i = C \frac{dv}{dt}\).
Formula / Reaction:$$\text{If } v(t) = V_0 \sin(\omega t), \quad i(t) = I_0 \cos(\omega t) = I_0 \sin\left(\omega t + \frac{\pi}{2}\right)$$
Solution:- When alternating voltage is applied to a capacitor, charge flows onto the plates immediately, so current reaches its peak before voltage builds up across the plates.
- Therefore, current leads the applied voltage by a phase angle of \(90^\circ\) (or \(\pi/2\text{ radians}\)).
Why other options are incorrect:- Opt_A: Current and voltage are in-phase only in a pure resistor (\(\phi = 0^\circ\)).
- Opt_C: Voltage leads current by \(90^\circ\) in a pure inductor, not a capacitor.
- Opt_D: A \(180^\circ\) phase lead represents complete phase opposition, which does not occur in a pure capacitor.
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