Question

What value resistor will discharge a 2.80μF capacitor to 10.0% of its initial charge in 3.00ms ?

Part A What value resistor will discharge a 2.80 MuF capacitor to 10.0% of its initial charge in 3.00ms?

Answer 1

The expression for the voltage decay in an \(\mathrm{RC}\) circuit is given as follows:

\(V=V_{.} e^{\frac{t}{R C}}\)

Rearrange the expression for the voltage drop as follows:

\(\begin{aligned} R &=\frac{t}{C \ln \frac{V_{0}}{V}} \\ &=\frac{3.00 \times 10^{-3} \mathrm{~s}}{\left(2.80 \times 10^{-6} \mathrm{~F}\right) \ln \frac{1}{10 / 100}} \\ &=465.1 \Omega \end{aligned}\)