First slide

Capacitance

Question

A condenser of capacity C₁ is charged to V volt. The energy stored in it is U. It is connected in parallel to another condenser of capacity C₂. The energy loss in this process will be

Moderate

A

$\frac{{UC}_{1}}{C_{1} + C_{2}}$
B

$\frac{{UC}_{2}}{C_{1} + C_{2}}$
C

${(\frac{C_{1}}{C_{1} + C_{2}})}^{2} U$
D

$\frac{{UC}_{1} C_{2}}{C_{1} + C_{2}}$

Solution

$U = \frac{1}{2} C_{1} V^{2}$
The energy loss is given by
$ΔE = \frac{1}{2} (\frac{C_{1} C_{2}}{C_{1} + C_{2}}) V^{2} = \frac{{UC}_{2}}{C_{1} + C_{2}}$

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