# A capacitance C, a resistance R and an emf ϵ are connected in series at t = 0. What is the maximum value of(a) the potential difference across the resistor,(b) the current in the circuit,(c) the potential difference across the capacitor,(d) the energy stored in the capacitor,(e) the power delivered by the battery and(f) the power converted into heat.

Energy stored in a capacitor:

The energy stored in a capacitor with capacitance C , charge is given by:

where V is the potential difference across the capacitor.

Power supplied by the battery:

If a battery of emf ϵ gives a current I, then the power supplied by the battery is given by:

Kirchhoff’s loop rule:

The sum of potential differences around a closed loop is zero.

Potential Difference (V) across a resistor of resistance R when current I passes through it is given by Ohm’s law:

(a)

By Kirchhoff’s loop rule,

As ϵ is constant,

At t = 0, there is no charge on the capacitor. Hence . So, Vr is maximum at t = 0.

(b) Initially, current flows through the circuit treating capacitor as short-circuit. But as charge accumulates on the capacitor the current reduces with time. It is maximum at t =0.

Using Kirchhoff’s loop rule,

I is max at t = 0 and

(c)

Using Kirchhoff’s loop rule,

As R and ϵ are constant

Current is minimum at equilibrium when capacitor acts as an open switch and current is zero. Hence,

(d)

The energy stored by the capacitor is given by:

As C is constant,

We know from (c) that the maximum potential difference across the capacitor is ϵ. Hence,

(e)

Power delivered by the battery is given by:

As ϵ is a constant,

Using the result from (b), we get

(f)

The resistor converts energy into heat:

As R is constant,

Now, using the result from (b),

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
Electric field inside cavity37 mins
Electric Flux - Theory46 mins
Test Your Knowledge of Electric Charge & Coulomb's Law47 mins
Check your knowledge of Electric Potential | Quiz45 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