Q. 70

How many time constants will elapse before the current in a charging RC circuit drops to half of its initial value? Answer the same question for a discharging RC circuit.

Answer :

Current when capacitor is discharging:


A capacitor of capacitance C is being discharged through a 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 current through the circuit at anytime t>0 is given by:



Where I0 is the initial current.


Note that is known as time constant


Current when capacitor is charging:


A capacitor of capacitance C is being charged using a battery of emf ϵ through a 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 current through the circuit at anytime t>0 is given by:



Where I0 is the initial current.


Note that is known as time constant.


In both the cases wish to find time t>0 such that



I(t) is given by the same formula in both the cases.







Hence, 0.69 time constants will elapse.


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