A 1 uF capacitor, intially charged to 50 V, discharges through a 1 Mohm resistor

Question

A 1 uF capacitor, intially charged to 50 V, discharges through a 1 Mohm resistor. A) write an equation expressing the charge on the capacitor as a function of time as it discharges.
B) how long does it take for the capacitor to lose 2/3 of its original charge. A 1 uF capacitor, intially charged to 50 V, discharges through a 1 Mohm resistor. A) write an equation expressing the charge on the capacitor as a function of time as it discharges.
B) how long does it take for the capacitor to lose 2/3 of its original charge. A) write an equation expressing the charge on the capacitor as a function of time as it discharges.
B) how long does it take for the capacitor to lose 2/3 of its original charge.

Explanation / Answer

Here ,

time constant , T = RC

T = 1 *10^-6 * 1 *10^6

T =1 s

For discharging of a capacitor ,

Q = Qo*(e^(-t/T))

Q = 1*50 e^(-t/1)

Q = 50*e^(-t)   uC

the expression of charge is 50*e^(-t)   uC

2)

here , for Q = Qo - 2Qo/3

Q = Qo/3

Qo/3 = Qo*(e^(-t/1))

1/3 = e^(-t)

taking ln

t = 1.1 s

time taken is 1.1 s

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