Physics Electrostatics ETEA 2018
PMDC Verified Question 108 of 131
Q.101 Two determine the resistance of a voltmeter by discharging a capacitor through it, the instantaneous voltage is then given by the relation:
A
\( V_o e^{-t/RC} \)
B
\( V_o e^{+t/RC} \)
C
\( V_o / 2 \)
D
\( V_o / \sqrt{2} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option A: \( V_o e^{-t/RC} \)
1. Concept:

When a capacitor discharges through a resistor (in this case, the internal resistance of the voltmeter), the voltage across it undergoes exponential decay.

2. Formula:

$$ V(t) = V_o e^{-t/RC} $$

3. Solution:

  • During discharge, the potential difference must decrease from its initial value \( V_o \) down toward zero.


  • This relies on a negative exponent where time (\( t \)) is divided by the time constant (\( \tau = RC \)).


4. Why other options are incorrect:

Option B represents exponential growth (voltage heading to infinity), which is physically impossible in a passive RC circuit. Options C and D only represent single arbitrary points in time, not the general instantaneous relation.

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