Before adjusting an electronics experiment, you want to make sure a capacitor yo

Question

Before adjusting an electronics experiment, you want to make sure a capacitor you've been using is fully discharged. (Otherwise, you might get a nasty shock!) During the experiment, the 4.10e-5 F capacitor was charged by a 5.0 V potential difference. When you turn the experiment off, the capacitor discharges through a 2.0×104 O resistor. Mathematically speaking, the capacitor never fully discharges; however, practically speaking, we might consider the capacitor to be "fully discharged" when the charge left on it is less than the magnitude of the charge of a single electron: -1.6×10-19 C. How long do you have to wait after turning the experiment off for this to occur?

Explanation / Answer

Initial charge    Q0   = CV    =   ( 4.1*10-5 F)(5.0V)   = 20.5*10-5 C    time constant = RC = ( 2.0*104 ) ( 4.1*10-5 F) = 0.82 s Condition for discharging of a capacitor          Q   =   Q0  e-t/ Here Q =   1.6*10-19 C          Q   Q0   =   e-t/    ==>   Q0 / Q    =   et/       ==> t = ln (  Q0 / Q  )       plug all values we get                    Solving for time t =   28.52 s    time constant = RC = ( 2.0*104 ) ( 4.1*10-5 F) = 0.82 s Condition for discharging of a capacitor          Q   =   Q0  e-t/ Here Q =   1.6*10-19 C          Q   Q0   =   e-t/    ==>   Q0 / Q    =   et/       ==> t = ln (  Q0 / Q  )       plug all values we get                    Solving for time t =   28.52 s

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