Question

. A 24-V battery is attached to a 3.0-mF capacitor and a 100-ohm resistor. If the capacitor is initially uncharged, what is the voltage across the capacitor 0.16 seconds after the circuit is connected to the battery

Answer 1

The voltage is
`V_c = 9.92 \ V`

Step-by-step explanation:

From the question we are told that

The voltage of the battery is
`V_b = 24 \ V`

The capacitance of the capacitor is
`C = 3.0 mF = 3.0 *10^(-3) \ F`

The resistance of the resistor is
`R = 100\ \Omega`

The time taken is
`t = 0.16 \ s`

Generally the voltage of a charging charging capacitor after time t is mathematically represented as

`V_c = V_o (1 - e^{- (t)/(RC) })`

Here
`V_o` is the voltage of the capacitor when it is fully charged which in the case of this question is equivalent to the voltage of the battery so

`V_c = 24 (1 - e^{- (0.16)/(100 * 3.0 *10^(-1)) })`

`V_c = 9.92 \ V`