# 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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Electrostatics of Conductors50 mins
Electric Dipole46 mins
Test Your Knowledge of Electric Charge & Coulomb's Law47 mins
Check your knowledge of Electric Potential | Quiz45 mins
Electric field inside cavity37 mins
Electric Flux - Theory46 mins
Interaction Quiz on Electic Potential50 mins
Electric Charges and Fields - 0556 mins
10 Problems on related to Electric Field & Charges41 mins
Electric Charges and Fields - 0854 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses