COMEDK · Physics · 23. Alternating Current

When an alternating voltage source \(V=100 \sin \left(100 \pi t+\frac{\pi}{6}\right)\) is applied to a pure capacitor of \(1 \mu \mathrm{~F}\), then the instantaneous value of current through capacitor is

A \(0.01 \pi \sin \left(100 \pi t+\frac{\pi}{3}\right)\)
B \(0.01 \pi \sin \left(100 \pi t+\frac{\pi}{6}\right)\)
C \(0.04 \pi \sin \left(100 \pi t+\frac{\pi}{3}\right)\)
D \(0.04 \pi \sin \left(100 \pi t+\frac{\pi}{6}\right)\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(0.01 \pi \sin \left(100 \pi t+\frac{\pi}{3}\right)\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \text { } V=100 \sin \left(100 \pi t+\frac{\pi}{6}\right) \\ & \therefore \phi_1=\frac{\pi}{6} \end{aligned}\) Since, alternating current leads \(\frac{\pi}{2}\) angle from alternating voltage in purely capacitive circuit, hence phase angle of alternating…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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