What is the Half-Life of a Discharged Capacitor?

[MegaDeth]

Homework Statement

A 100 micro F capacitor is discharged through a resistor of resistance 470K Ohms. Determine the 'half-life' of this circuit. The half life being the time it takes for the initial voltage to decrease by 50%.

Homework Equations

Is my answer correct? If not, what have I done wrong?

The Attempt at a Solution

Here's what I've done:

Using V = V(Initial)e^-(t/RC)
Since the initial V is double V, divide both sides by V which will result in, 0.5 = e^-(t/RC).
RC (time constant) = 47 seconds

Taking natural logs of both sides and re-arranging gives:

47*ln(0.5) = - t
so t = 32.6 seconds

 

[CWatters]

Looks ok to me.

As a check... the time constant of an RC circuit is very roughly = R * C

In this case R * C = 47 seconds which isn't a million miles away from 32 seconds.

See also..

http://en.wikipedia.org/wiki/RC_time_constant

PS: Large real world capacitors typically have a large manufacturing tollerance (20 to 80%) so somerimes R*C is as accurate as you need to get. It's a different matter for small capacitors which can be accurate to a few percent.