If there is a series combination of a resistor and an initially charged capacitor, I know that the decay of the voltage is given by the equation v(t) = Ae^(-t/RC) where V(0) = A = V0. But i am unsure of how to get to this equations.
If I assume Ir = current flowing through resistor
and Ic = current flowing through Capacitor and assume there both flowing out of the node.
The Attempt at a Solution
Ic + Ir = 0
C(dv/dt) + V/R = 0
V/R = -C(dv/dt)
1/V(dv) = -1/RCdt
integrate both sides
ln v = -t/RC + A
A= integration constant
Here is where i cant go no more I saw somewhere they got: ln v = -t/RC + ln A, from there I know how to get the solution but how to arrive at ln A?, can we just do this automatically because it is a constant to make life easier or is there some logic behind it?