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A capacitor of 2 muF is charged to 200 V and another of 3 muF is charged to 100 V. They are connected with opposite polarities, i.e. the positive…

Numerical answer

A capacitor of

2\ \mu\mathrm{F}

is charged to

200\ \mathrm{V}

and another of

3\ \mu\mathrm{F}

is charged to

100\ \mathrm{V}

. They are connected with opposite polarities, i.e. the positive plate of each joined to the negative plate of the other. The energy lost (in mJ) in the connecting process is ______.

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Answer: 54

Initial charges:

q_1 = 2\times200 = 400\ \mu\mathrm{C}

and

q_2 = 3\times100 = 300\ \mu\mathrm{C}

. With opposite polarities the net charge is

400-300 = 100\ \mu\mathrm{C}

on the combined capacitance

5\ \mu\mathrm{F}

, so the common voltage is

V = 20\ \mathrm{V}

. Initial energy:

\tfrac12(2)(200)^2 + \tfrac12(3)(100)^2 = 40000+15000 = 55000\ \mu\mathrm{J} = 55\ \mathrm{mJ}

. Final energy:

\tfrac12(5)(20)^2 = 1000\ \mu\mathrm{J} = 1\ \mathrm{mJ}

. Loss

= 55-1 = 54\ \mathrm{mJ}

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