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Question: If potential difference of a condenser \((6\mu F)\) is changed from 10 V to 20 V then increase in en...

If potential difference of a condenser (6μF)(6\mu F) is changed from 10 V to 20 V then increase in energy is

A

2×10−4J2 \times 10^{- 4}J

B

4×10−4J4 \times 10^{- 4}J

C

3×10−4J3 \times 10^{- 4}J

D

9×10−4J9 \times 10^{- 4}J

Answer

9×10−4J9 \times 10^{- 4}J

Explanation

Solution

Initial energy Ui=12CV12U_{i} = \frac{1}{2}CV_{1}^{2};

Final energy Uf=12CV22U_{f} = \frac{1}{2}CV_{2}^{2}

∴ Increase in energy

ΔU=Uf−Ui=12C(V22−V12)=12×6×10−6(202−102)=9×10−4J.\Delta U = U_{f} - U_{i} = \frac{1}{2}C(V_{2}^{2} - V_{1}^{2}) = \frac{1}{2} \times 6 \times 10^{- 6}(20^{2} - 10^{2}) = 9 \times 10^{- 4}J.