Two identical 2.5-$\varOmega$ resistors are parallel to each other,and the combination is in series with a 5.0-nF capacitor,in a circuit with a switch open.If initially 15.0 V is across the capacitor,how long after the switch is closed will the voltage across the resistor pair be 2.5 V?
A)1.1 ns
B)11 ns
C)4.4 ns
D)44 ns

Question

Quizplus · Accepted Answer

The time constant of the circuit is given by:

τ = RC = (2.5 Ω + 2.5 Ω) × 5.0 nF = 25 ps

When the switch is closed, the capacitor will start to discharge through the resistor pair. The voltage across the resistor pair as a function of time can be described by:

V(t) = V0 × exp(-t/τ)

where V0 is the initial voltage across the capacitor. We want to find the time when the voltage across the resistor pair is 2.5 V, so we can write:

2.5 V = 15.0 V × exp(-t/τ)

Solving for t, we get:

t = -τ × ln(2.5/15.0) = 11 ns

Therefore, the answer is B.

Two Identical 2 Ω\varOmegaΩ Resistors Are Parallel to Each Other,and the Combination Is in the Combination

Two Identical 2 $\varOmega$ Resistors Are Parallel to Each Other,and the Combination Is in the Combination