First slide

Capacitance

Question

Two insulated metallic spheres of 3 $μ$ F and 5 $μ$ F capacitances are charged to 300 V and 50 V respectively. The energy loss, when they are connected by a wire, is

Easy

A

0.012 J
B

0.0218 J
C

0.0375 J
D

3.75 J

Solution

The energy loss when the capacitors are connected by a wire
$\begin{array}{l} = \frac{1}{2} [\frac{C_{1} C_{2}}{C_{1} + C_{2}} {(V_{1} - V_{2})}^{2}] \\ = \frac{1}{2} [\frac{(3 \times 10^{- 6}) (5 \times 10^{- 6})}{(3 \times 10^{- 6}) + (5 \times 10^{- 6})} (300 - 50)^{2}] = 0 .0375 J \end{array}$

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