A capacitor of capacitance 2 F is charged to potential V; its stored energy is E₁. It is then connected in parallel to an identical uncharged capacitor. If the final energy is E₂, the ratio E₂/E₁ is:
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Question

A capacitor of capacitance 2 F is charged to potential V; its stored energy is E₁. It is then connected in parallel to an identical uncharged capacitor. If the final energy is E₂, the ratio E₂/E₁ is:

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G1 Physics · Accepted Answer

Initial charge Q = CV and E₁ = (1/2)CV². After connection to an identical uncharged capacitor, total capacitance is 2C and common voltage is V/2 by charge conservation. E₂ = (1/2)(2C)(V/2)² = CV²/4. Thus E₂/E₁ = (CV²/4)/(CV²/2) = 1/2.