Question

Help with capacitor question?

The time constant, `tau`, of a capacitor of capacitance `C` which discharges through a resistor of resistance `R` is given by: `tau = RC`

Calculate the time taken for a capacitor to discharge to `1%` of its initial charge, given that `C = 0.01xx10^-6 F` and `R = 330xx10^3Omega`?

Answer 1

`t = 0.0152" s"`

Explanation:

Exponential discharge is:

`Q(t) = Q(0)e^(-t/(RC))`

We are told that `(Q(t))/(Q(0)) = 1% = 0.01`

`0.01 = Q(0)e^(-t/(RC))`

ln(0.01) = -t/(RC)

`t = -RCln(0.01)`

`t = -(330xx10^3" "Omega)(0.01xx10^-6" F")ln(0.01)`

`t = 0.0152" s"`