discharging a capacitor Discharging a capacitor During a physics demonstration,

Question

discharging a capacitor

Discharging a capacitor During a physics demonstration, a fully charged 2.00 mF capacitor is discharged through a 60.0 Ohm resistor. If the capacitor had initially been charged using a 12-volt battery, what was its initial charge, and how much energy was stored in it? How long does it take for the capacitor to lose half of its initial charge? How long does it take for the capacitor to lose half of its initial stored energy? How long does it take for the capacitor to lose 99.9% of its initial charge?

Explanation / Answer

a) Q = CV = 2.0E-3*12=36.0E-3 C

E = 1/2 C V^2 = 0.5*2.0E-3*12^2=0.144 J

b) Q = Q0 e^(-t/tau)

e^(-t/tau) = 1/2

t = - tau*ln(0.5) = -2.0E-3*60*ln(0.5)=0.0832 s

C) loses half it energy when Q = Q0/sqrt(2) since E = Q^2/2X

so t = -2.0E-3*60*ln(1/sqrt(2))=0.0416 s

d) so 0.01% is left

t=-2.0E-3*60*ln(0.001)=0.8289 s

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