Question

A capacitor has 10 V initially across and it is instantaneously connected to a resistor. What is the voltage across the capacitor after one time constant?

Answer 1

Answer:

3.69 V

Explanation:

By connecting across the resistor, the capacitor starts discharging.

The voltage across the capacitor when discharging is given by

$V = V_0e^{-t/T}$

V is the voltage across it at time t,

$V_0$ is the initial voltage when fully charged,

T is the time constant

After one time constant, t = T. Then

$V = V_0e^{-T/T}= 0.369V_0$

From the question, $V_0 =10 \text{ V}$

$V = 10\text{ V}\times0.369 = 3.69 \text{ V}$