An RC circuit consists of a resistor with resistance 1.0 k $\varOmega$ , a 120-V battery, and two capacitors, C1 and C2, with capacitances of 20.0 µF and 60.0 µF, respectively. Initially, the capacitors are uncharged; and the switch is closed at t = 0 s.
-Determine the total charge on both capacitors two time constants after the switch is closed.

Question

An RC circuit consists of a resistor with resistance 1.0 k

\varOmega

, a 120-V battery, and two capacitors, C1 and C2, with capacitances of 20.0 µF and 60.0 µF, respectively. Initially, the capacitors are uncharged; and the switch is closed at t = 0 s.
-Determine the total charge on both capacitors two time constants after the switch is closed.

Quizplus · Accepted Answer

The capacitors are in series, so the equivalent capacitance is given by 1/C_eq = 1/C1 + 1/C2. Solving gives C_eq = 15 µF. The time constant τ = R * C_eq = 1.0 kΩ * 15 µF = 15 ms. After two time constants, the charge on the capacitors is Q = C_eq * V * (1 - e^(-2)) ≈ 8.3 × 10^-3 C.

An RC Circuit Consists of a Resistor with Resistance 1 Ω\varOmegaΩ

An RC Circuit Consists of a Resistor with Resistance 1 $\varOmega$