How long will it take a 0.047 $\mu \mathrm { F }$ capacitor to completely discharge through a 10 $k \Omega$ resistor?
A) 0.47 ms
B) 2.35 ms
C) 5 s
D) 0.18 ms

Question

How long will it take a  0.047  $\mu \mathrm { F }$ capacitor to completely discharge through a 10 $k \Omega$ resistor?
A)  0.47 ms
B)  2.35 ms
C)  5 s
D)  0.18 ms

Quizplus · Accepted Answer

The time constant (τ) for this circuit is calculated by using the formula τ = R x C, where R is the resistance and C is the capacitance. Plugging in the given values, we get:
τ = (10 kΩ)(0.047 μF) = 0.47 ms
After one time constant, the capacitor will be discharged to about 63% of its initial voltage, and after 5 time constants it will be almost completely discharged. Since we are asked for the time to completely discharge the capacitor, we need to find the time it takes for the capacitor to go through 5 time constants:
5τ = 5(0.47 ms) = 2.35 ms
Therefore, the time it takes for the capacitor to completely discharge through the 10 kΩ resistor is 2.35 ms.

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