A capacitance C charged to a potential difference V is discharged by connecting its plates through a resistance R. Find the heat dissipated in one time constant after the connections are made. Do this by calculating `int i^(2)Rdt`and also by finding the decrease in the energy stored in the capacitor.

Explanation

Energy stored at a part time in discharging
` = 1/2 cv^2 (1 - t/rc)^2 `
` Heat dissipated at any time `
= Energy stored at time 0
- energy stored at time `t`
` = 1/2 cv^(2) - 1/2 cv^2 (e^-1)^2 `
`= 1/2 (cv^2) (1- (e^-2))` .