- #1

Brute

- 8

- 0

## Homework Statement

Hi,

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.

## Homework 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

Then:

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 can't 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?