In a charging RC circuit, what happens to the capacitor voltage Vc(t) as t becomes very large?

In a charging RC circuit, what happens to the capacitor voltage Vc(t) as t becomes very large?

• A. 0
• B. Vs/2
• C. Vs/3
• D. Vs

Answer: (D)

In charging a DC RC circuit, the capacitor voltage climbs toward the applied source voltage because the current through the resistor dies away as the capacitor charges. The voltage across the capacitor follows Vc(t) = Vs(1 − e^(−t/RC)). As t becomes very large, the exponential term e^(−t/RC) goes to zero, so Vc(t) approaches Vs. At that steady state, the current is zero, which means no voltage is dropped across the resistor—the entire source voltage sits across the capacitor. So the final capacitor voltage is Vs.

In charging a DC RC circuit, the capacitor voltage climbs toward the applied source voltage because the current through the resistor dies away as the capacitor charges. The voltage across the capacitor follows Vc(t) = Vs(1 − e^(−t/RC)). As t becomes very large, the exponential term e^(−t/RC) goes to zero, so Vc(t) approaches Vs. At that steady state, the current is zero, which means no voltage is dropped across the resistor—the entire source voltage sits across the capacitor. So the final capacitor voltage is Vs.