Q. 71

How many time constants will elapse before the charge on a capacitor falls to 0.1% of its maximum value in a discharging RC circuit?

Answer :

Concepts/Formulas used:


Charge on Capacitor during Discharging (RC Circuit):


A capacitor of capacitance with charge C is being discharged through a resistor of resistance R. A switch S is also connected in series with the capacitor. The switch is initially open. At t=0, the switch is closed. The charge on the capacitor at any time t>0 is given by:



where and Qi is the initial charge on the capacitor.


Note that the capacitor begins charging at t = 0.


Capacitance:


If two conductors have a potential difference V between the them and have charges Q and -Q respectively on them, then their capacitance is defined as



Let a capacitor of capacitance C be discharged through a resistor of resistance R. Switch S in attached is series and in initially open. It is closed at t = 0.


Charge is maximum when the capacitor is fully charged. Hence,



Now, we have at any time t>0,



We want to find t such that







Hence, we need 6.9 time constants.


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