Two identical circuits have a capacitor in series with a resistor and a switch. In circuit A, the resistor has resistance R, while in circuit B, its resistance is 4R. The capacitors are identical. Each capacitor begins fully charged, and each circuit is open. When each circuit is completed (i.e., the switch in them is closed), the capacitor will begin to discharge. If a time t is required for circuit A's capacitor to fully discharge (say, by 99%), what time will be required for circuit B's capacitor to do the same?
A) 4t
B) 2t
C) t
D) 0.5t
E) 0.25t

Question

Quizplus · Accepted Answer

The time required for a capacitor to discharge through a resistor is determined by the time constant, τ = RC. Since circuit B has a resistor with 4 times the resistance (4R) of circuit A, its time constant is 4 times larger, meaning it will take 4 times longer to discharge by the same amount.

Two Identical Circuits Have a Capacitor in Series with a Resistor