Physics Electrostatics UHS 2023
PMDC Verified Question 30 of 131
Q.147 A capacitor of capacitance 'C' has a charge 'Q' and stored energy is 'W'. If the charge is increased to '2Q'. The stored energy will be:
A
2W
B
4W
C
W/4
D
W/2
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: 4W
1. Concept:

The energy within a capacitor scales quadratically with the total amount of charge it possesses (provided its physical capacitance remains unchanged).

2. Formula:

$$ W = \frac{Q^2}{2C} $$

3. Solution:

  • The original stored energy equation is \( W = \frac{Q^2}{2C} \).


  • When charge is doubled to \( 2Q \), plug it in: \( W' = \frac{(2Q)^2}{2C} = \frac{4Q^2}{2C} \).


  • Factoring out the original expression yields \( W' = 4 \times W \).


4. Why other options are incorrect:

Option A falsely assumes energy scales linearly with charge (\( U \propto Q \)). Options C and D represent decreases, which physically contradicts forcing more charge into the plates.

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