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Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

Document Description: Energy Stored in a Capacitor for NEET 2022 is part of Physics Class 12 preparation. The notes and questions for Energy Stored in a Capacitor have been prepared according to the NEET exam syllabus. Information about Energy Stored in a Capacitor covers topics like and Energy Stored in a Capacitor Example, for NEET 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Energy Stored in a Capacitor.

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Energy Stored in a Charged capacitor

Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

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 Class 12 - NEET

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

Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

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

Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

This work is stored as the potential energy,

Therefore, Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

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

Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

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 Class 12 - NEET

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 Class 12 - NEET

or Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

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 Class 12 - NEET

Therefore, Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

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 Class 12 - NEET Q = CV (C = equivalent capacitance)

so W = CV × V = CV2

Now energy on the capacitor Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

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 Class 12 - NEET Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET          Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

Charge flow through battery = Qf - Qi

= 2CV - CV = CV

H = (CV × 2V) - Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

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 Class 12 - NEET Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

Finally let q charge flows clockwise then

Now applying KVL

Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET 
    Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

5q + 50 + 5q - 200 + 2q = 0

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

so finally
Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

 

(b) Find heat loss in the above circuit.

ΔH = Energy [initially - finally] on capacitor

Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEETEnergy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

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 Class 12 - NEET Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

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 Class 12 - NEET

Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

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 Class 12 - NEET = Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

(b) Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

(c) Heat loss during redistribution :

Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

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 Class 12 - NEET Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

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 Class 12 - NEET

Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

= Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

H = Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET      Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

when oppositely charged terminals are connected then

Therefore, C1V C2V = C1V1 - C2V2

Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

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 Class 12 - NEET Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

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 Class 12 - NEET                   

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 Class 12 - NEET

(ii) Heat produced = Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET × 2 × (20)2   Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET × 3 × (10)2 - Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET × 5 × (14)2

= 400 150 - 490

= 550- 490 = 60 mJ

Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

  • 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 Class 12 - NEET Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

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 Class 12 - NEET

  • 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 Class 12 - NEET          Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET                Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET 

Sol. Let charge flow is q.

Now applying Kirchhoff's voltage low

Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET     

     Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

- 2q = - 25

q = 12.5 mC

Final charges on plates

    Energy Stored in a Capacitor Notes | Study Physics Class 12 - NEET

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