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A capacitor of capacitance C, which is i...

A capacitor of capacitance C, which is initially uncharged , is connected with a battery of emf `epsilon`. Find the heat dissipated in the circuit during the process of charging .

Text Solution

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Let R be the net resistance of the circuit.
During charging the charge on the capacitor varies as
`q= q_(0)(1-e^(-1//RC))`, wehre `q_(0)= epsilonC`
As `i= (dq)/(dt) implies i= ( epsilon)/(R ) (e^(-1//RC))`
Thermal power is given by `(dH)/(dt) = i^(2) Rimplies H = int i^(2) Rdt= (epsilon^(2))/(R^(2)) xx R int_(0)^(infty)e^(-2t//RC) dt `
gt H = ( epsilon^(2))/(R) [ (e^(-2 t //RC))/(2//RC)]_(0)^(infty)=(Cepsilon^(2))/(2) [-e^(-2t//RC)]_(0)^(infty) = (1)/(2) Cepsilon^(2) [ 1-0] = (1)/(2) C epsilon^(2)`
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