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

3.69 V

Step-by-step 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}*0.369 = 3.69 \text{ V}`