Consider the situation shown in figure (31-E23 ) . The switch S is open for a long time and then closed . (a) Find the charge flown through the battery when the switch S is closed (b)Find the work done by the battery .

Explanation

Since a switch is open for long time , the capacitor is in series
Hence ` = C_eq = C / 2 `
When the switch is closed , charge flow
` C / 2 xx eplison = C eplison / 2 `
(b) Work done `= 2 xx v `
` = C eplsion / 2 xx eplison = C eplison^(2) / 2`
( c) The change of energy stored `= 1 /2 C_eq xx v^(2) `
` = 1 /2 xx C / 2 xx eplison ^(2) = 1 / 4 C eplison ^(2)`
(d) The change in energy `= Heat developed `
` 1 / 4 C eplsion ^(2) `