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Question

# Effective capacitance of parallel combination of two capacitors C1 and C2 is 10 μF. When these capacitors are individually connected to a voltage source of 1 V, the energy stored in the capacitor C2 is 4 times that of C1. If these capacitors are connected in series, their effective capacitance will be:

A
4.2 μF
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B
3.2 μF
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C
1.6 μF
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D
8.4 μF
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Solution

## The correct option is C 1.6 μFIn parallel combination, Ceq=C1+C2=10 μF−−−(1) When connected across 1 V battery, Given that, U1U2=(12C1V2)(12C2V2)=14 ⇒C1C2=14−−−(2) From, (1) and (2), ⇒C2=8 μF and C1=2 μF Now C1 and C2 are connected in series combination, ∴Cequivalent=C1C2C1+C2=2×82+8 ⇒Cequivalent=1610=1.6 μF Hence, option (C) is correct.

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