Return to the example of the capacitor C discharging through the resistor R, whi

Question

Return to the example of the capacitor C discharging through the resistor R, which was worked out in Section 4.11, and show that the total energy dissipated in the resistor agrees with the energy originally stored in the capacitor. Suppose someone objects that the capacitor is never really discharged because Q becomes zero only for t = ?. How would you counter this objection? You might find out how long it would take the charge to be reduced to one electron, with some reasonable assumptions. Return to the example of the capacitor C discharging through the resistor R, which was worked out in Section 4.11, and show that the total energy dissipated in the resistor agrees with the energy originally stored in the capacitor. Suppose someone objects that the capacitor is never really discharged because Q becomes zero only for t = ?. How would you counter this objection? You might find out how long it would take the charge to be reduced to one electron, with some reasonable assumptions. Return to the example of the capacitor C discharging through the resistor R, which was worked out in Section 4.11, and show that the total energy dissipated in the resistor agrees with the energy originally stored in the capacitor. Suppose someone objects that the capacitor is never really discharged because Q becomes zero only for t = ?. How would you counter this objection? You might find out how long it would take the charge to be reduced to one electron, with some reasonable assumptions.

Explanation / Answer

lets consider with some practical values:

R=100k ohms

C=1 uF

time constant=T=R*C=0.1 seconds

let initial charge be 1 uC.

charge at any time t is given by 1 uC*exp(-t/T)

let at time t,

charge =charge on one electron=1.6*10^(-19)

==>1.6*10^(-19)=10^(-6)*exp(-t/T)

==>exp(-t/T)=1.6*10^(-13)

==>-t/0.1=-29.464

==>t=2.9464 seconds

so it wont become 0 at t=inifnity and at a very high time constant, it will drop to sufficiently low value.

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