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 Q_{i} 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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A parallel-plate capacitor has plate area 20 cm^{2}, plate separation 1.0 mm and a dielectric slab of dielectric constant 5.0 filling up the space between the plates. This capacitor is joined to a battery of emf 6.0 V through a 100 kΩ resistor. Find the energy for the capacitor 8.9 μs after the connections are made.

How many time constants will elapse before the energy stored in the capacitor reaches half of its equilibrium value in a charging RC circuit?

HC Verma - Concepts of Physics Part 2