Question

An RC circuit is composed of the following components:

- Resistor: R = 12 KΩ
- Battery Voltage: 12 V
- Capacitor C1 with capacitance 10μF
- Capacitor C2 with capacitance 25μF

Determine the time constant (τ) in seconds for the circuit.

Options:
A) 4.2×10⁵
B) 2.5
C) 0.30
D) 0.085
E) 0.42

Answer 1

The time constant for the given RC circuit, after finding the equivalent capacitance of the two capacitors in series, is 0.085 seconds, which corresponds to option D in the question.

Step-by-step explanation:

To determine the time constant (τ) for an RC circuit with two capacitors in series, one must first find the equivalent capacitance. Capacitors in series are calculated using the reciprocal formula: ⅖ = ⅖ + ⅖. Here, the capacitors are 10μF and 25μF. Their equivalent capacitance (Ceq) is given by:

1 / Ceq = (1 / 10μF) + (1 / 25μF) = 0.1mF⁻¹ + 0.04mF⁻¹ = 0.14mF⁻¹.

Thus, Ceq = 1 / 0.14mF⁻¹ ≈ 7.14μF.

The resistor value is given as R = 12 KΩ. The time constant for an RC circuit is defined as τ = RC. Substituting the resistance and the equivalent capacitance:

τ = 12 kΩ × 7.14μF = 12,000 Ω × 7.14 × 10⁻¶ F = 0.08568 ≈ 0.086 seconds.

The correct answer to this RC circuit question is option D) 0.085.