Problem 10. (4 points) Discharging a capacitor in an RC circuit. How long will i

Question

Problem 10. (4 points) Discharging a capacitor in an RC circuit. How long will it take a charged 40-F capacitor to lose 30% of its initial energy when it is allowed to discharge through a 90- resistor?
(A) 0.93 ms
(B) 0.65 ms
(C) 0.41 ms
(D) 0.20 ms

Problem 10. (4 points) Discharging a capacitor in an RC circuit. How long will it take a charged 40-uF capacitor to lose 30% of its initial energy when it is allowed to discharge through a 90-Q resistor? (A) 0.93 ms (B) 0.65 ms (C) 0.41 ms (D) 0.20 ms

Explanation / Answer

here,

let the potential across the capacitor is Vo

for the final potential Vf

when 30 % energy is lost

0.50 * C * V^2 = 0.50 * C * Vo^2 * (1 - 0.30)

V = 0.84 * Vo

NOw, let the time taken is t

time constant , T = R * C

T = 40 *10^-6 * 90 = 3.6 ms

Now, as V = Vo * e^(-t/T)

0.84 *Vo = Vo * e^(-t/T)

0.84=e^(-t/3.6)

solving for t

t = 0.65 ms

the time taken is B) 0.65 ms

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