A resistor, capacitor, and switch are all connected in series to an ideal battery of constant terminal voltage. Initially, the switch is open. What is the voltage across the resistor and the capacitor at the moment the switch is closed?

The options to the question asked are listed below

A) The voltage across both the resistor and the capacitor is zero.

B) The voltage across the resistor is zero, and the voltage across the capacitor is equal to the terminal voltage of the battery.

C) The voltage across both the resistor and the capacitor is equal to the terminal voltage of the battery.

D) The voltage across the resistor is equal to the terminal voltage of the battery, and the voltage across the capacitor is zero.

E) The voltage across both the resistor and the capacitor is equal to one-half of the terminal voltage of the battery.

Answer:

D. The voltage across the resistor is equal to the terminal voltage of the battery, and the voltage across the capacitor is zero.

Explanation:

As soon as the switch is closed, the capacitor starts to charge through the resistor. At the moment the switch is closed, the voltage across the resistor equals the terminal voltage and the voltage across the capacitor equals zero. As the time, t increases, the capacitor begins to get charged and the voltage across it increases based on the formula

Vc=Vt (1-e^ (-t/Rc)) where Vt is the terminal voltage and Vc is the voltage across the capacitor.