A 0.20-mF capacitor discharges through a resistor with R = 61 k$\varOmega$.How long will it take for the capacitor to reach 85% of its initial charge?
A)0.5 s
B)4.2 s
C)0.25 s
D)1.98 s
E)33.2 s

Question

A 0.20-mF capacitor discharges through a resistor with R = 61 k$\varOmega$.How long will it take for the capacitor to reach 85% of its initial charge? 
A)0.5 s 
B)4.2 s 
C)0.25 s 
D)1.98 s 
E)33.2 s

Quizplus · Accepted Answer

The time constant of the circuit is given by:

τ = RC = (61 kΩ)(0.20 μF) = 12.2 ms

To find the time it takes for the capacitor to reach 85% of its initial charge, we can use the formula:

V = V0e^(-t/τ)

where V is the voltage across the capacitor after time t, V0 is the initial voltage across the capacitor, and e is the mathematical constant approximately equal to 2.718.

Solving for t:

0.85V0 = V0e^(-t/τ)

Taking the natural logarithm of both sides:

ln(0.85) = -t/τ

Solving for t:

t = -ln(0.85) τ = -ln(0.85) (61 kΩ)(0.20 μF) ≈ 1.98 ms

Therefore, the answer is D) 1.98 s.

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