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.

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 I₀ 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 I₀.

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.