Question

Using the exact exponential treatment, what is the time required to discharge a 270 µF capacitor through a 500 Ω resistor down to 1.00% of its original voltage?

a. 2.303 seconds
b. 4.606 seconds
c. 6.909 seconds
d. 9.212 seconds

Answer 1

The time required to discharge the capacitor is 4.606 seconds.

Step-by-step explanation:

The time required to discharge a capacitor through a resistor can be found using the formula t = RC, where t is the time constant, R is the resistance, and C is the capacitance. In this case, the capacitance is given as 270 µF and the resistance is 500 Ω. Multiplying these values gives the time constant:

t = 270 µF * 500 Ω = 0.135 seconds

To find the time required to discharge the capacitor down to 1.00% of its original voltage, we can use the formula V = Vo * e^(-t/RC), where V is the final voltage, Vo is the initial voltage, t is the time, R is resistance, and C is capacitance. Rearranging the formula to solve for time, we have:

t = -RC * ln(V/Vo)

Substituting the given values, we get:

t = -500 Ω * 270 µF * ln(0.01) = 4.606 seconds