The current flowing out of the capacitor as it undergoes discharge, and therefor

Question

The current flowing out of the capacitor as it undergoes discharge, and therefore through the resistor, is I(t) = dQ/dt Write out explicitly I(t). (Only C, t, R, and V_0 will appear in the answer.) The instantaneous power dissipated in the resistor as the capacitor is being discharged is P(t) = R[I(t)]^2 Write out explicitly P(t). (Only C, t, R, and V_0 will appear in the answer.) The total energy dissipated in the resistor during the entire capacitor is discharge is U = integral_0^infinity P(t) dt Calculate U. (Only C and V_0 will appear in the answer.) Compare the answers to questions 7 and 12. What do you notice? What fundamental law of physics does this support?

Explanation / Answer

10) for the discharing capacitor

I = dQ/dt

I = d/dt(C * Vo * ( e^(-t/(R * C))))

I = Vo/R * ( e^(-t/(R * C)))

11) for the power

Power = R * I^2

Power = R * (Vo/R * ( e^(-t/(R * C))))^2

12) for the total energy dissispated

total energy = integration(R * (Vo/R * ( e^(-t/(R * C))))^2). dt from 0 to infinite

total energy = 0.5 * C * Vo^2

13) We notice that the answers for both are same

Yes , this support the conservation of energy principle

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