Physics Alternating Current PMDC Conceptual Practice
PMDC Verified Question 56 of 127
An alternating voltage \(v(t) = V_0 \sin(\omega t)\) is connected across an ideal capacitor. What is the expression for the instantaneous alternating current \(i(t)\)?
A
\(i(t) = I_0 \sin(\omega t)\)
B
\(i(t) = I_0 \sin\left(\omega t - \frac{\pi}{2}\right)\)
C
\(i(t) = -I_0 \sin(\omega t)\)
D
\(i(t) = I_0 \sin\left(\omega t + \frac{\pi}{2}\right)\)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: \(i(t) = I_0 \sin\left(\omega t + \frac{\pi}{2}\right)\)
Concept:

In an ideal capacitor, current leads the applied voltage by \(90^\circ\) (\(\pi/2\text{ rad}\)).

Formula / Reaction:

$$i = C \frac{dv}{dt} = C \frac{d}{dt}[V_0 \sin(\omega t)] = \omega C V_0 \cos(\omega t) = I_0 \sin\left(\omega t + \frac{\pi}{2}\right)$$

Solution:

  • Since current reaches its peak before voltage, its phase argument is \(\omega t + \frac{\pi}{2}\).


Why other options are incorrect:

  • Opt_A: In-phase current for a resistor.


  • Opt_B: Lagging current for an inductor.


  • Opt_C: Phase inversion (\(180^\circ\)).

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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