# Problem: A 20 μF capacitor initially charged to 25 μC is discharged through a 1.1 kΩ resistor. How long does it take to reduce the capacitor's charge to 10 μC?

###### FREE Expert Solution

The time constant in the series RC circuit is:

$\overline{){\mathbf{\tau }}{\mathbf{=}}{\mathbf{R}}{\mathbf{C}}}$, where R is the equivalent resistance, C is the equivalent capacitance, and τ is the time constant.

The final charge stored by the capacitor is expressed as:

$\overline{){\mathbf{Q}}{\mathbf{=}}{{\mathbf{Q}}}_{{\mathbf{0}}}{{\mathbf{e}}}^{\mathbf{-}\mathbf{t}}{\mathbf{\tau }}}}$, where Q is the final charge and Q0 is the initial charge stored by the capacitor.

To find time constant, R = 1.1 kΩ = 1.1 × 103Ω and

C = 20 μF = 20 × 10-6F

τ = (1.1 × 103)(20 × 10-6) = 0.022s

###### Problem Details

A 20 μF capacitor initially charged to 25 μC is discharged through a 1.1 kΩ resistor. How long does it take to reduce the capacitor's charge to 10 μC?