Question

An emf source with a magnitude of E = 120 V, a resistor with a resistance of R = 85.0 Ω, and a capacitor with a capacitance of C = 2.20 μF are connected in a circuit. Calculate the time constant of the circuit.

Answer 1

The time constant of the circuit with a resistor of 85.0 Ω and a capacitor of 2.20 μF is calculated as 0.187 seconds, which represents the time for the capacitor to charge to about 63.2% of the emf.

Step-by-step explanation:

The student has asked how to calculate the time constant of a circuit consisting of an emf source, a resistor, and a capacitor. The time constant (τ) of an RC circuit is given by the product of the resistance (R) and the capacitance (C), mathematically expressed as τ = RC. Using the provided values, R = 85.0 Ω and C = 2.20 μF, we can calculate the time constant.

τ = RC = (85.0 Ω) * (2.20 μF) = 85.0 * 2.20 * 10-6 = 0.187 ΩF

So, the time constant of the circuit is 0.187 seconds. This indicates the time it takes for the capacitor to charge to approximately 63.2% of the final voltage when connected to an emf source through a resistor.