Question

When discharging a capacitor, as discussed in conjunction with Figure 21.39, how long does it take for the voltage on the capacitor to reach zero? Is this a problem?

Short answer

Infinite time, the small remaining charge can leak.

Step-by-step solution

Discharging a capacitor

The discharging of the capacitor is,

\({\rm{V = }}{{\rm{V}}_{\rm{0}}}{{\rm{e}}^{\frac{{{\rm{ - t}}}}{{{\rm{RC}}}}}}\)

Here,\({{\rm{V}}_{\rm{0}}}\)is the voltage across the capacitor when it is charged to the maximum,\({\rm{t}}\)is the time from the initiation of discharging,\({\rm{R}}\)is the resistance in the circuit, and\({\rm{C}}\)is the value of capacitance of the capacitor.

 Step 2: Explanation

The capacitor discharges as \({{\rm{e}}^{{\rm{ - t}}}}\), which means that it decays exponentially with time.

However, because it is asymptotic to the zero line on the charge axis, this variable never approaches zero.

This is a concern since a small amount of charge stays in the capacitor, which can lead to problems such as static leakage and other problems.