Chapter 29, Problem 1ASA

To determine

The voltage across the capacitor in the in dc and the RC circuits.

Answer to Problem 1ASA

The voltage across the capacitor in the dc is charged up to the supply voltage until it is discharged from the resistor and voltage across the capacitor in the $RC$ circuit opposes the battery.

Explanation of Solution

The RC circuit is the circuit that contains resistor as well as the capacitor, the capacitor stores the charge an is an electrical component. When the switch is closed in the circuit, the charge increases on the capacitor plate. The charge that is attained by the capacitor is proportional to the applied voltage across  it. In the RC circuits, when the battery is connected that is switched on then the charging of the capacitor depends upon the applied voltage.

Write the expression for the voltage across the capacitor.

  $V=\frac{Q}{C}$

Here, $V$ is the voltage across the capacitor, $Q$ is the amount of charge that is stored on plate and $C$ is the capacitance.

The voltage here opposes the battery  when the emf goes from zero to maxium value.

In the dc circuit, when there is both resistor and the capacitor, the voltage and the current change with time, the capacitor is charged upto its supply voltage, but in dc it blocks the current through it that is because of the dielectric of the capacitor is insulator that is non conductive. The voltage across the capcitor change in the continuous manner, the capacitor has the effect of holding up a voltage once they are charged to it, until the voltage is discharged through the resistor.

Conclusion:

Thus, the voltage across the capacitor in the dc is charged up to the supply voltage until it is discharged from the resistor and voltage across the capacitor in the $RC$ circuit opposes the battery.