A series RC circuit has a time constant of 0.900 s. The battery has an emf of 24.0 V, and the maximum current in the circuit is 0.500 mA.
-What is the capacitance?
A)1.80 μF
B)43.2 μF
C)18.8 μF
D)53.3 μF

Question

Quizplus · Accepted Answer

We can use the formula for the time constant of an RC circuit:
τ = RC
where τ is the time constant, R is the resistance in ohms, and C is the capacitance in farads.

We are given τ = 0.900 s and the maximum current I = 0.500 mA, which we can convert to I = 0.000500 A.

From the formula for the maximum current in an RC circuit, we have:
I = ε/R
where ε is the emf of the battery.

Substituting ε = 24.0 V and solving for R, we get:
R = ε/I = 24.0 V / 0.000500 A = 48000 Ω

Substituting R and τ into the formula for the time constant, we get:
τ = RC = (48000 Ω)(C) = 0.900 s

Solving for C, we get:
C = τ/R = 0.900 s / 48000 Ω = 1.875 × 10^-5 F = 18.8 μF

Therefore, the answer is choice C.

A Series RC Circuit Has a Time Constant of 0