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Qmechanic
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Let a capacitor be connected to a battery in a circuit.The The battery does work worth CV^2$CV^2$ but the capacitor stores only half that amount....We We say the other half went away as heat,but but how do we mathematically show where the other half went.?

Let a capacitor be connected to a battery in a circuit.The battery does work worth CV^2 but the capacitor stores only half that amount....We say the other half went away as heat,but how do we mathematically show where the other half went.

Let a capacitor be connected to a battery in a circuit. The battery does work worth $CV^2$ but the capacitor stores only half that amount... We say the other half went away as heat, but how do we mathematically show where the other half went?

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Discrepancy in capacitor

Let a capacitor be connected to a battery in a circuit.The battery does work worth CV^2 but the capacitor stores only half that amount....We say the other half went away as heat,but how do we mathematically show where the other half went.