E = 1500 V , R = 85.0 k?, and C = 3500 ?F We know the constant for the circuit t

Question

E = 1500 V , R = 85.0 k?, and C = 3500 ?F

We know theconstant for the circuit t= 296 s.

We know themaximum charge that will appear on the capacitor is 5.25 C.

We know the time it will take for the capacitor to acquire a charge of 250.0 milli-coulomb is 14.5 s.

Question:Assume that that the capacitor in this problem has been fully charged. It is then disconnected from the circuit and a 5.00 kilo-ohm resistor connected in parallel with itto discharge it. How long will it take to be completely discharged? Give your answer in the form "ab.c s".

Explanation / Answer

After the capacitor has been fully charged, its voltage will be that of the battery, i.e., 1500V

So, now as the capacitor is connected to a resistor, current will start flowing through the resistor.

Hence, applying Kirchoff's voltage law, we get

(Q/C + rac{dQ}{dt} R =0 )

(Q_{t} = Q_{0} e^{-t/RC}) , where Q0 = initial charge of capacitor, Qt = charge at time "t"

Dividing by C, we get

(V_{t} = V_{0} e^{-t/RC}) , where V0 = initial voltage of capacitorVt = voltage of capacitor at time "t"

hence,

(V_{t} = 1500 e^{-t/17.5})

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