Q. 695.0( 2 Votes )

# A 100 μF capacitor is joined to a 24 V battery through a 1.0 MΩ resistor. Plot qualitative graphs

(a) between current and time for the first 10 minutes and

(b) between charge and time for the same period.

Answer :

Charging a capacitor:

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. The capacitor is uncharged at first. At t=0, the switch is closed. The current through the circuit at anytime t>0 is given by:

Where I_{0} is the initial current.

The charge is given by:

Note that is known as time constant.

Given,

Resistance of the resistor,

Capacitance,

Emf of the battery,

Now, time constant ,

(a)

The current is given by:

At t =0, we have y-intercept I_{0}.

Now,

Hence, we need to plot

At t = 10min = 600s,

(b)

Now,

Note that the current is in Ampere and time in seconds. The graph will represent exponential decay.

We need to plot

Note that t is in seconds and Q in coulombs.

At t = 10 min = 600s,

The charge will keep on increasing and will almost touch the asymptope at Q = 0.0024C.

Rate this question :

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