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

Answer:

The  voltage is $V_c = 9.92 \ V$

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

       $V_c = V_o (1 - e^{- \frac{t}{RC} })$

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  

      $V_c = 24 (1 - e^{- \frac{0.16}{100 * 3.0 *10^{-1}} })$

      $V_c = 9.92 \ V$