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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 Vac is
and the potential difference Vcb is
This is a differential equation whose solution is
as can be verified by differentiation and substitution into 5). Since Q = C E, 6) becomes