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.

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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