We know that voltage across a capacitor is given by
But there is this other formula
How this second formula was deducted mathematically from the first one? or from another one?
Electrical Engineering Stack Exchange is a question and answer site for electronics and electrical engineering professionals, students, and enthusiasts. It only takes a minute to sign up.Sign up to join this community
Let I_r be current in the resistor = Vc/R at any time.
Vc = Q/C from the basic definition of capacitance.
dQ/dt = -I_r = -Vc/R From the basic definition of current.
dQ/dt = -Q/CR
Apply initial conditions, Q at time 0 = Vs * C and do trivial calculus, then substitution to get Vc in place of Q.