Physics Electrostatics PMDC 2021
PMDC Verified Question 89 of 131
Q.116 In series combination of capacitors
A
\( C_1 + C_2 + C_3 \)
B
\( \frac{C_1 C_2}{C_1 + C_2} \)
C
\( \frac{C_1 + C_2}{C_1 C_2} \)
D
\( \frac{1}{C_1 + C_2 + C_3} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: \( \frac{C_1 C_2}{C_1 + C_2} \)
1. Concept:

When capacitors are linked in series, their combined ability to store charge decreases, acting reciprocally.

2. Formula:

$$ \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} $$

3. Solution:

  • Find a common denominator to add the fractions: \( \frac{1}{C_{eq}} = \frac{C_2 + C_1}{C_1 C_2} \).


  • To find the actual equivalent capacitance (\( C_{eq} \)), you must invert the entire fraction.


  • Result: \( C_{eq} = \frac{C_1 C_2}{C_1 + C_2} \) (Product over Sum rule).


4. Why other options are incorrect:

Option A is the formula for Parallel capacitors. Option C is mathematically \( 1/C_{eq} \), forgetting the final necessary inversion. Option D is an invalid algebraic mashup.

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