JEE  >  Physics For JEE  >  Energy Stored in a Capacitor

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Document Description: Energy Stored in a Capacitor for JEE 2022 is part of Electrostatic Potential and Capacitance for Physics For JEE preparation. The notes and questions for Energy Stored in a Capacitor have been prepared according to the JEE exam syllabus. Information about Energy Stored in a Capacitor covers topics like and Energy Stored in a Capacitor Example, for JEE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Energy Stored in a Capacitor.

Introduction of Energy Stored in a Capacitor in English is available as part of our Physics For JEE for JEE & Energy Stored in a Capacitor in Hindi for Physics For JEE course. Download more important topics related with Electrostatic Potential and Capacitance, notes, lectures and mock test series for JEE Exam by signing up for free. JEE: Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE
1 Crore+ students have signed up on EduRev. Have you?

Energy Stored in a Charged capacitor

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Work has to be done in charging a conductor against the force of repulsion by the already existing charges on it. The work is stored as a potential energy in the electric field of the conductor. Suppose a conductor of capacity C is charged to a potential V0 and let q0 be the charge on the conductor at this instant. The potential of the conductor when (during charging) the charge on it was q (< q0) is,

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Now, work done in bringing a small charge dq at this potential is,

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Therefore, total work done in charging it from 0 to q0 is,

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

This work is stored as the potential energy,

Therefore, Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Further by using q0 = CV0 we can write this expression also as,

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

In general if a conductor of capacity C is charged to a potential V by giving it a charge q, then

 Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

3.1 Energy Density of a Charged Capacitor

This energy is localized on the charges or the plates but is distributed in the field. Since in case of a parallel plate capacitor, the electric field is only between the plates, i.e., in a volume (A × d), the energy density

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

or Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

3.2 Calculation of Capacitance

The method for the calculation of capacitance involves integration of the electric field between two conductors or the plates which are just equipotential surfaces to obtain the potential difference Vab. Thus,

 Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Therefore, Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

3.3 Heat Generated :

(1) Work done by battery

W = QV

Q = charge flow in the battery

V = EMF of battery

(2) W = Ve (When Battery discharging)

W = -Ve (When Battery charging)

(3) Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE Q = CV (C = equivalent capacitance)

so W = CV × V = CV2

Now energy on the capacitor Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Therefore, Energy dissipated in form of heat (due to resistance)

H = Work done by battery - {final energy of capacitor - initial energy of capacitor}

Ex.3 At any time S1 switch is opened and S2 is closed then find out heat generated in circuit.

Sol.

 Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE          Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Charge flow through battery = Qf - Qi

= 2CV - CV = CV

H = (CV × 2V) - Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Ex.4 (a) Find the final charge on each capacitor if they are connected as shown in the figure.

Sol. Initially 

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Finally let q charge flows clockwise then

Now applying KVL

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE 
    Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

5q + 50 + 5q - 200 + 2q = 0

12 q - 150 = 0 ⇒ Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

so finally
Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

 

(b) Find heat loss in the above circuit.

ΔH = Energy [initially - finally] on capacitor

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEEEnergy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Distribution of Charges on Connecting two Charged Capacitors :

When two capacitors C1 and C2 are connected as shown in figure

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Before connecting the capacitors

Parameter

Ist Capacitor

IInd Capacitor

Capacitance

C1

C2

Charge

Q1

Q2

Potential

V1

V2

 

After connecting the capacitors

Parameter

Ist Capacitor

IInd Capacitor

Capacitance

C1

C2

Charge

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Potential

V1

V2


(a) Common potential :

By charge conservation on plates A and C before and after connection.

Q1 +  Q2 = C1V  + C2V

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE = Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

(b) Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

(c) Heat loss during redistribution :

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

The loss of energy is in the form of Joule heating in the wire. 

  • When plates of similar charges are connected with each other ( with and - with -) then put all values (Q1, Q2, V1, V2) with positive sign.
  • When plates of opposite polarity are connected with each other ( with -) then take charge and potential of one of the plate to be negative.

 Derivation of above formulae :

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Let potential of B and D is zero and common potential on capacitors is V, then at A and C it will be V.

C1V +  C2V = C1V1 + C2V2

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

= Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

H = Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE      Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

when oppositely charged terminals are connected then

Therefore, C1V C2V = C1V1 - C2V2

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Ex.5 Find out the following if A is connected with C and B is connected with D.

(i) How much charge flows in the circuit.

(ii) How much heat is produced in the circuit.

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Sol. Let potential of B and D is zero and common potential on capacitors is V, then at A and C it will be V.

By charge conservation,

3V + 2V = 40 + 30

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE                   

5V = 70 ⇒ V = 14 volt 

Charge flow = 40 - 28 = 12 μC

Now final charges on each plate is shown in the figure.

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

(ii) Heat produced = Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE × 2 × (20)2   Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE × 3 × (10)2 - Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE × 5 × (14)2

= 400 150 - 490

= 550- 490 = 60 mJ

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

  • When capacitor plates are joined then the charge remains conserved.
  • We can also use direct formula of redistribution as given above.

Ex.6 Repeat above question if A is connected with D and B is connected with C.

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

Sol. Let potential of B and C is zero and common potential

on capacitors is V, then at A and D it will be V

2V +   3V = 10 ⇒ V = 2 volt

Now charge on each plate is shown in the figure.

Heat produced = 400 + 150 - 1

Therefore 2 × 5 × 4

= 550 - 10 = 540 μJ

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

  • Here heat produced is more. Think why ?

Ex.7 Three capacitors as shown of capacitance 1mF, 2mF and 2mF are charged upto potential difference 30 V, 10 V and 15V respectively. If terminal A is connected with D, C is connected with E and F is connected with B. Then find out charge flow in the circuit and find the final charges on capacitors.

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE          Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE                Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE 

Sol. Let charge flow is q.

Now applying Kirchhoff's voltage low

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE     

     Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

- 2q = - 25

q = 12.5 mC

Final charges on plates

    Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

The document Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE is a part of the JEE Course Physics For JEE.
All you need of JEE at this link: JEE
199 videos|531 docs|256 tests
Download as PDF

Download free EduRev App

Track your progress, build streaks, highlight & save important lessons and more!

Related Searches

Important questions

,

mock tests for examination

,

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

,

Semester Notes

,

study material

,

Previous Year Questions with Solutions

,

Viva Questions

,

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

,

Free

,

shortcuts and tricks

,

pdf

,

Objective type Questions

,

Exam

,

Summary

,

MCQs

,

Extra Questions

,

Energy Stored in a Capacitor Notes | Study Physics For JEE - JEE

,

ppt

,

Sample Paper

,

past year papers

,

video lectures

,

practice quizzes

;