Question
Consider two identicalcapacitors with capacitance C. One is charged with charge Q and hasa potential difference of V across its plates. The second capacitoris uncharged. We then connect the second to the first - the leftplate to the left plate and the right plate to the right plate. Asa result, the second capacitor becomes charged. Since energy isconserved, the energy in the two capacitors (after they areconnected) equals the energy stored in the first capacitor (beforethey are connected).
If this statement is true, prove it. Iffalse, show why it is false.
Explanation / Answer
Common potential after connected V ' = [ C V + C (0 ) ] / ( C + C ) = V / 2 Since the two capacitors are connected to parallel. Energy stored in first capacitor( before they are connected) E = ( 1/ 2) C V 2 Energy stored in second capacitor( before they areconnected ) E = 0 Total energy before connected = ( 1/ 2) C V2 Energy stored in second capacitor( before they areconnected ) E = 0 Total energy before connected = ( 1/ 2) C V2 Energy stored in first capacitor( after they areconnected ) E ' = ( 1/ 2) C ( V/2) 2 = ( 1/ 4 ) ( 1/ 2) C V 2 Energy stored in second capacitor( after theyare connected ) E " = ( 1/ 2) C ( V/2) 2 = ( 1/ 4 ) ( 1/ 2) C V 2 Total energy after connected = ( 1/ 4 ) ( 1/ 2) C V2 + ( 1/ 4 ) ( 1/ 2) C V 2 = ( 1/ 2 ) ( 1/ 2) C V 2 = ( 1/ 4 ) C V 2 So, energy not conserved . = ( 1/ 4 ) ( 1/ 2) C V 2 Energy stored in second capacitor( after theyare connected ) E " = ( 1/ 2) C ( V/2) 2 = ( 1/ 4 ) ( 1/ 2) C V 2 Total energy after connected = ( 1/ 4 ) ( 1/ 2) C V2 + ( 1/ 4 ) ( 1/ 2) C V 2 = ( 1/ 2 ) ( 1/ 2) C V 2 = ( 1/ 4 ) C V 2 So, energy not conserved . So, energy not conserved .