A capacitor of capacitance C is given a charge Q. At `t=0`,it is connected to an uncharged of equal capacitance through a resistance R. Find the charge on the second capacitor as a function of time.

Explanation

Let after time t charge on plate A is Q- q
`
V_A = (Q-q/C) V_B = (q/C) `
` V_A -V_B = (Q-q/C) -q/C `
` =Q-2q/CR `
` Current = dq/dt = (Q-2q/CR) `
` rArr dq/(Q-2q) = 1/RC dt `
` (dq/Q-2q)= 1/RC dt `
` dq/(Q-2q)= 1/RC dt `
` 1/2 [ In (Q-2q)-InQ] = -1t/RC `
` In (Q-2q/Q) = -2t/RC`
` Q- 2q = Q e^(-2t/RC)`
` 2q = Q(1-e^(-2t/RC))`
` q = { 1- e^(2t/2C)}