Physics Electronics PMDC Conceptual Practice
PMDC Verified Question 287 of 494
During the non-conducting interval of a rectifier with a parallel shunt capacitor filter, the capacitor discharges through the load resistance \( R_L \) according to which time-dependent equation?
A
v(t) = Vm × exp(-t / (RL C))
B
v(t) = Vm × (1 - exp(-t / (RL C)))
C
v(t) = Vm × cos(ω t)
D
v(t) = Vm × (t / (RL C))
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option A: v(t) = Vm × exp(-t / (RL C))
Concept:

When the input AC voltage drops below the capacitor voltage, the diode turns OFF and the capacitor discharges stored charge into the load resistor \( R_L \) with an exponential decay time constant \( \tau = R_L C \).

Formula:

$$v_C(t) = V_m \exp\left(-\frac{t}{R_L C}\right) \approx V_m \left(1 - \frac{t}{R_L C}\right) \quad (\text{for } t \ll R_L C)$$

Solution:

  • The capacitor charges to peak voltage \( V_m \) during diode conduction.


  • When the diode turns OFF, the capacitor discharges through \( R_L \) according to \( v(t) = V_m e^{-t / (R_L C)} \).


  • A larger time constant \( R_L C \) slows this discharge, reducing output ripple.


Why other options are incorrect:

  • Option B: \( V_m(1 - e^{-t/RC}) \) describes capacitor charging from a DC source, not discharging.
  • Option C: The discharge is governed by an exponential decay, not an AC cosine wave.
  • Option D: Linear decay is only an approximation for the initial portion of the exponential curve.

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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