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Prove. In the circuit of Fig. 11 containing resistance R, capacitance C and a source of emf E, let q represent the charge on the capacitor at a certain instant after the switch S is closed, and let i be the current in the circuit at that instant. Then the amount of charge on the capacitor at some subsequent time t is given by

where Q = C E.

Proof. The potential difference V_{ac} is

and the potential difference V_{cb} is

Thus

or

This is a differential equation whose solution is

as can be verified by differentiation and substitution into 5). Since Q = C E, 6) becomes

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