Physics Electrostatics NUMS 2024
PMDC Verified Question 22 of 131
Q.199 Capacitor cannot be fully charge because time required to charge
A
1 time constant
B
2 times constant
C
4 times constant
D
Infinity
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: Infinity
1. Concept:

The charging curve of a capacitor in a standard DC circuit follows an asymptotic exponential growth function.

2. Formula:

$$ Q(t) = Q_{max} \left( 1 - e^{-t/RC} \right) $$

3. Solution:

  • As the capacitor fills, the opposing voltage it generates reduces the incoming current.


  • Mathematically, the term \( e^{-t/RC} \) only truly reaches exactly 0 when time (\( t \)) reaches absolute mathematical infinity.


  • Thus, while practically it is considered "fully charged" after roughly 5 time constants, theoretically, it requires infinite time.


4. Why other options are incorrect:

At 1 time constant, it is ~63% charged. At 4 time constants, it is ~98% charged. Neither represents a "full" 100% mathematical charge.

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