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Contact [7]
3 years ago
11

A parallel-plate capacitor is charged and then is disconnected from the battery. By what factor does the stored energy change wh

en the plate separation is then doubled?
Physics
1 answer:
andrew-mc [135]3 years ago
5 0

Answer:

0.5

Explanation:

The energy of a charged capacitor is given by \frac{1}{2}QC where Q is the charge on it and C is its capacitance. The capacitance is defined, geometrically, as

\dfrac{\epsilon A}{d}

where \epsilon is a constant that is determined by the material between the plates, A is the area of the plates and d is the distance between them. It is then that the capacitance is linearly inversely proportional to the separation distance; as the distance increases, the capacitance reduces.

Because it is linear, when the separation distance is doubled, other factors remaining constant, the capacitance is halved. Because the capacitance is halved, the energy is halved.

Let's see the mathematics.

Initial capacitance, C_1 at initial separation, d_1

C_1=\dfrac{\epsilon A}{d_1}

If separation is doubled, separation becomes d_2=2d_1. Then the capacitance becomes

C_2=\dfrac{\epsilon A}{d_2}

C_2=\dfrac{\epsilon A}{2d_1}

C_2=0.5\dfrac{\epsilon A}{d_1}

C_2=0.5C_1

Initial energy, E_1=\frac{1}{2}QC_1

Final energy, E_2=\frac{1}{2}QC_2= \frac{1}{2}Q\times0.5C_1

E_2=0.5\times\frac{1}{2}QC_1=0.5E_1

Hence, \frac{E_2}{E_1}=0.5

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