First slide

Redistribution of charges and concept of common potential

Question

A 60 pF capacitor is fully charged by a 20 V supply. It is then disconnected from the supply and is connected to another uncharged 60 pF capacitor in parallel. The electrostatic energy that is lost in the process by the time the charge is redistributed between them is (in nJ) ____

Moderate

Solution

$V_{0} = 20 V$
Heat loss = $U_{1} - U_{f} = \frac{1}{2} C V_{0}^{2} - 2 [\frac{1}{2} C {(\frac{V_{0}}{2})}^{2}] = \frac{C V_{0}^{2}}{4}$
$= \frac{(60 \times 10^{- 12}) {(20)}^{2}}{4} J = 6 \times 10^{- 9} J = 6 n J$

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