A parallel plate capacitor of capacitance C is charged to a potential V. It is then connected to another uncharged capacitor having the same capacitance. Find out the ratio of the energy stored in the combined system to that stored initially in the single capacitor.

Solution

Energy stored in a capacitor is given by, $E space equals space 1 half Q squared over C$

When capacitor is connected in parallel combination, equivalent capacitance = 2C

Here, total charge Q remains the same.

Initial energy is given by, $straight E subscript straight i space equals space 1 half straight Q squared over straight C$

Final energy is given by, $straight E subscript straight f space equals space 1 half fraction numerator straight Q squared over denominator 2 straight C end fraction$

So, the ratio of energy is given by,
$fraction numerator F i n a l space e n e r g y over denominator I n i t i a l space e n e r g y end fraction equals space 1 half$

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Electrostatic Potential And Capacitance

A parallel plate capacitor of capacitance C is charged to a potential V. It is then connected to another uncharged capacitor having the same capacitance. Find out the ratio of the energy stored in the combined system to that stored initially in the single capacitor.

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