The plates of a capacitor are charged to a potential difference of $$100$$ V and then connected across a resistor. The potential difference across the capacitor decays exponentially with respect to time. After one second the potential difference between the plates of the capacitor is $$80$$ V. What is the fraction of the stored energy which has been dissipated?

Question

Infinity Learn · Accepted Answer

Energy loss Δ$$U=12CV02$$−$$12CV2Fractional$$ energy lossΔ$$UU0=12CV02$$−$$12CV212CV02=V02$$−$$V2V02=(100)2$$−$$(80)2(100)2=20$$×$$180(100)2=925=0.36$$

Capacitors and capacitance

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Capacitors and capacitance

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Energy loss ΔU=12CV02−12CV2Fractional energy lossΔUU0=12CV02−12CV212CV02=V02−V2V02=(100)2−(80)2(100)2=20×180(100)2=925=0.36

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