A series RC circuit has a time constant of 1.5 s.The battery has a voltage of 50 V and the maximum current just after closing the switch is 500 mA.The capacitor is initially uncharged.What is the charge on the capacitor 3.0 s after the switch is closed?
A) 0.48 C
B) 0.86 C
C) 0.43 C
D) 0.99 C

Question

A series RC circuit has a time constant of 1.5 s.The battery has a voltage of 50 V and the maximum current just after closing the switch is 500 mA.The capacitor is initially uncharged.What is the charge on the capacitor 3.0 s after the switch is closed? 
A) 0.48 C 
B) 0.86 C 
C) 0.43 C 
D) 0.99 C

Quizplus · Accepted Answer

We can use the formula for charge on the capacitor in an RC circuit:

Q = CV = Q₀(1 - e^(-t/τ))

Where:
Q₀ = initial charge on the capacitor (in this case, 0)
C = capacitance (not given, but not needed since we are looking for the ratio of Q/Q₀)
τ = time constant = RC = 1.5 s
t = time elapsed = 3.0 s

Plugging in the values, we get:

Q/Q₀ = 1 - e^(-3.0/1.5) = 0.432

Since Q₀ was 0, the charge on the capacitor after 3.0 s is simply 0.432 times the maximum charge that could be stored on the capacitor, which is:

Q = CV = ICt = (0.5 A)(3.0 s) = 1.5 C

So:

Q = 0.432 × 1.5 C = 0.648 C ≈ 0.43 C

Therefore, the best choice is (C) 0.43 C.

A Series RC Circuit Has a Time Constant of 1