The Question is from neet-physics electrostatics , and it was created by the author SUBHANI

Question

When two identical capacitors are in series have $3\,\mu F$ capacitance and when parallel $12\,\mu F.$ What is the capacitance of each

SUBHANI · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
	**Primary Concept**: Capacitance in series and parallel circuits
	**Related Topics**: Electric circuits, Energy storage
	**Prerequisites**: Basic knowledge of electrical components
## SOLUTION PATHWAY
**Given Information**:
		1. Two identical capacitors
		2. Series capacitance: $C_s = 3\,\mu F$
		3. Parallel capacitance: $C_p = 12\,\mu F$
**Method & Steps**:
	1.  Determine the capacitance of each capacitor in series:
		Reasoning: For capacitors in series, the total capacitance is given by the formula:
		$\frac{1}{C_s} = \frac{1}{C} + \frac{1}{C}$
		=> $C_s = \frac{C}{2}$
		Substituting the known value, we get:
		$\frac{1}{3\,\mu F} = \frac{1}{C} + \frac{1}{C}$
		=> $C = 6\,\mu F$.
	2.  Confirm the result using parallel capacitance:
		Reasoning: For capacitors in parallel, the total capacitance is:
		$C_p = C + C = 2C$
		Substituting:
		$12\,\mu F = 2C$ => $C = 6\,\mu F$.
	3.  Conclusion:
		Both methods confirm that the capacitance of each capacitor is $6\,\mu F$.
		Result: $C = 6\,\mu F$.
		Verification: Both series and parallel results lead to the same individual capacitance.
## OPTION ANALYSIS
[A] ✓: Correct option; the calculations confirm $C = 6\,\mu F$.
[B] :x: Incorrect; $3\,\mu F$ does not satisfy either series or parallel conditions.
[C] :x: Incorrect; $12\,\mu F$ is the total capacitance in parallel, not individual.
[D] :x: Incorrect; $9\,\mu F$ does not fit the series or parallel formulas.
## LEARNING AIDS
	**Common Mistakes**:
		1. Confusing series and parallel formulas: Remember, series adds inversely, parallel adds directly.
		2. Miscalculating total capacitance: Double-check calculations for each configuration.
	**Quick Tips**:
		1. Use the formula for each configuration and verify.
		2. Remember that identical capacitors simplify calculations significantly.

SUBHANI · Answer

The correct Option is "$6\,\mu {\rm{ }}F$"

SUBHANI · Answer

$3\,\mu {\rm{ }}F$

SUBHANI · Answer

$12\,\mu {\rm{ }}F$

SUBHANI · Answer

$9\,\mu {\rm{ }}F$

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