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.
-What is the time constant of the circuit?

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.
-What is the time constant of the circuit?

Quizplus · Accepted Answer

The time constant $\tau$ for an RC circuit is given by $\tau = R \times C_{eq}$, where $C_{eq}$ is the equivalent capacitance. For capacitors in series, $C_{eq} = \frac{1}{\frac{1}{C1} + \frac{1}{C2}}$. Here, $C_{eq} = \frac{1}{\frac{1}{20 \times 10^{-6}} + \frac{1}{60 \times 10^{-6}}} = 15 \times 10^{-6}$ F. Thus, $\tau = 1000 \times 15 \times 10^{-6} = 0.015$ s or 1.5 × 10^-2 s.

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

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