Capacitors in Series and Parallel Class 12 Notes | EduRev

Physics Class 12

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Class 12 : Capacitors in Series and Parallel Class 12 Notes | EduRev

The document Capacitors in Series and Parallel Class 12 Notes | EduRev is a part of the Class 12 Course Physics Class 12.
All you need of Class 12 at this link: Class 12

5. Capacitor Circuits

Ex.8 Find charge on each capacitor.

Capacitors in Series and Parallel Class 12 Notes | EduRev

Sol. Charge on C1 = C1V1 = 2 × (20 - 5)μC

Capacitors in Series and Parallel Class 12 Notes | EduRev

= 30 μC

Charge on C2 = C2V2 = 2 × (20 - (-10))μC

= 60 μC

Charge on C3 = C3V3 = 4 × (20 - 10)μC

= 40 μC

Ex.9 Find charge on each capacitor.  

Capacitors in Series and Parallel Class 12 Notes | EduRev

Sol. Charge on C1 = (x - 10) C1

Charge on C2 = (x - 0) C2

Charge on C3 = (x - 20) C3

Now from charge conservation at node x    

 Capacitors in Series and Parallel Class 12 Notes | EduRev

(x - 10)C1  (x - 0)C2  (x - 20)C3 = 0

⇒ 2x - 20 2x 4x - 80 = 0

⇒ x = 25 Therefore

so Capacitors in Series and Parallel Class 12 Notes | EduRev

Capacitors in Series and Parallel Class 12 Notes | EduRev

Capacitors in Series and Parallel Class 12 Notes | EduRev

Capacitors in Series and Parallel Class 12 Notes | EduRev

Ex.10 In the given circuit find out the charge on each capacitor. (Initially they are uncharged)

Capacitors in Series and Parallel Class 12 Notes | EduRev Capacitors in Series and Parallel Class 12 Notes | EduRev

Sol. Let potential at A is 0, so at D it is 30 V, at F it is 10 V and at point G potential is -25V. Now apply Kirchhoff's Ist law at point E. (total charge of all the plates connected to 'E' must be same as before i.e. 0)

Therefore, (x - 10) +  (x - 30) 2 +(x 25) 2 = 0

5x = 20

x = 4

Final charges :

Q2mF = (30 - 4) 2 = 52 mC

Q1mF = (10 - 4) = 6 mC

Q2mF = (4 - (-25)) 2 = 58 mC

Capacitors in Series and Parallel Class 12 Notes | EduRev

Ex.11 

Capacitors in Series and Parallel Class 12 Notes | EduRev

Find voltage across capacitor C1.

Sol. 

Capacitors in Series and Parallel Class 12 Notes | EduRev

Now from charge conservation at node x and y

for x

(x - 4)C1 + (x - 2)C2 + (x - y)C3 = 0 ⇒    

 2(x - 4) + 2(x - 2) (x - y) 2 = 0

6x - 2y - 12 = 0 .....(1)

For y

(y - x)C3 +  [y -(-4)]C4  (y - 0)C5 = 0 ⇒ (y - x)2 (y 4) 2 y 2 = 0

= 6y - 2x 8 = 0 .....(2)

eq. (1) & (2)

y = - 3 Therefore 

 x = 7 Therefore 

So potential difference = x - y = Capacitors in Series and Parallel Class 12 Notes | EduRev Capacitors in Series and Parallel Class 12 Notes | EduRev

6. Combination of Capacitors :

6.1 Series Combination :

(i) When initially uncharged capacitors are connected as shown, then the combination is called series combination

Capacitors in Series and Parallel Class 12 Notes | EduRev

(ii) All capacitors will have same charge but different potential difference across then.

(iii) We can say that

Capacitors in Series and Parallel Class 12 Notes | EduRev

V1 = potential across C1

Q = charge on positive plate of C1

C1 = capacitance of capacitor similarly

Capacitors in Series and Parallel Class 12 Notes | EduRev

(iv) V1 : V2 : V3Capacitors in Series and Parallel Class 12 Notes | EduRev

We can say that potential difference across capacitor is inversely proportional to its capacitance in series combination.

Capacitors in Series and Parallel Class 12 Notes | EduRev

Note :  In series combination the smallest capacitor gets maximum potential.

(v) Capacitors in Series and Parallel Class 12 Notes | EduRevCapacitors in Series and Parallel Class 12 Notes | EduRevCapacitors in Series and Parallel Class 12 Notes | EduRev

Where V = V1 +   V2 + V3

(vi) Equivalent Capacitance :

Equivalent capacitance of any combination is that capacitance which when connected in place of the combination stores same charge and energy as that of the combination

In series :

Capacitors in Series and Parallel Class 12 Notes | EduRev ........................

In series combination equivalent is always less then smallest capacitor of combination.

(vii) Energy stored in the combination

UcombinationCapacitors in Series and Parallel Class 12 Notes | EduRev

UcombinationCapacitors in Series and Parallel Class 12 Notes | EduRev

Energy supplied by the battery in charging the combination

Ubattery = Q × V = Q . Capacitors in Series and Parallel Class 12 Notes | EduRev = Capacitors in Series and Parallel Class 12 Notes | EduRev

Capacitors in Series and Parallel Class 12 Notes | EduRev

Half of the energy supplied by the battery is stored in form of electrostatic energy and half of the energy is converted into heat through resistance.

Derivation of Formulae :

Capacitors in Series and Parallel Class 12 Notes | EduRev

Meaning of equivalent capacitor

Capacitors in Series and Parallel Class 12 Notes | EduRev

Capacitors in Series and Parallel Class 12 Notes | EduRev

Now,

Initially, the capacitor has no charge. Applying Kirchhoff's voltage law

Capacitors in Series and Parallel Class 12 Notes | EduRev

Capacitors in Series and Parallel Class 12 Notes | EduRev

Capacitors in Series and Parallel Class 12 Notes | EduRev

Capacitors in Series and Parallel Class 12 Notes | EduRev

Capacitors in Series and Parallel Class 12 Notes | EduRev

in general

Capacitors in Series and Parallel Class 12 Notes | EduRev

Ex.12 Three initially uncharged capacitors are connected in series as shown in circuit with a battery of emf 30V. Find out following :

(i) charge flow through the battery,

(ii) potential energy in 3 mF capacitor. 
Capacitors in Series and Parallel Class 12 Notes | EduRev

(iii) Utotal in capacitors 

(iv) heat produced in the circuit

Sol. Capacitors in Series and Parallel Class 12 Notes | EduRev

Ceq = 1 μF.

(i) Q = Ceq V = 30 μC

(ii) charge on 3μF capacitor = 30 μC

energy = Capacitors in Series and Parallel Class 12 Notes | EduRev = Capacitors in Series and Parallel Class 12 Notes | EduRev = 150 μJ

(iii) UtotalCapacitors in Series and Parallel Class 12 Notes | EduRev = 450 μJ

(iv) Heat produced = (30 μC) (30) - 450 μJ = 450 μJ

Ex.13 Two capacitors of capacitance 1 mF and 2mF are charged to potential difference 20 V and 15 V as shown in figure. If now terminal B and C are connected together terminal A with positive of battery and D with negative terminal of battery then find out final charges on both the capacitor.

Capacitors in Series and Parallel Class 12 Notes | EduRev  Capacitors in Series and Parallel Class 12 Notes | EduRev

Capacitors in Series and Parallel Class 12 Notes | EduRev

Now applying kirchhoff voltage law

Capacitors in Series and Parallel Class 12 Notes | EduRev

- 40 - 2q - 30 - q = - 60

3q = - 10

Charge flow = - Capacitors in Series and Parallel Class 12 Notes | EduRev μC.

Charge on capacitor of capacitance 1μF = 20 q = Capacitors in Series and Parallel Class 12 Notes | EduRev

Charge on capacitor of capacitance 2μF = 30 q = Capacitors in Series and Parallel Class 12 Notes | EduRev

6.2 Parallel Combination :

(i) When one plate of one capacitor is connected with one plate of the other capacitor, such combination is called parallel combination.

(ii) All capacitors have same potential difference but different charges.

(iii) We can say that :

Q1 = C1V

Q1 = Charge on capacitor C1

C1 = Capacitance of capacitor C
Capacitors in Series and Parallel Class 12 Notes | EduRev

V = Potential across capacitor C1

(iv) Q1 : Q2 : Q3 : C1 : C2 : C3

The charge on the capacitor is proportional to its capacitane Q µ C

(v) Capacitors in Series and Parallel Class 12 Notes | EduRev

Capacitors in Series and Parallel Class 12 Notes | EduRev

Capacitors in Series and Parallel Class 12 Notes | EduRev

Where Q = Q1 + Q2 + Q3 ..............

Capacitors in Series and Parallel Class 12 Notes | EduRev

  • Maximum charge will flow through the capacitor of largest value.

(vi) Equivalent capacitance of parallel combination

Ceq = C1  C2  C3

  • Equivalent capacitance is always greater then the largest capacitor of combination.

(vii) Energy stored in the combination :

Capacitors in Series and Parallel Class 12 Notes | EduRev

Capacitors in Series and Parallel Class 12 Notes | EduRev = Capacitors in Series and Parallel Class 12 Notes | EduRev

Capacitors in Series and Parallel Class 12 Notes | EduRev

Capacitors in Series and Parallel Class 12 Notes | EduRev

  • Half of the energy supplied by the battery is stored in the form of electrostatic energy and half of the energy is converted into heat through resistance.

Formulae Derivation for parallel combination :

Q = Q1  Q2  Q3

= C1V C2V C3V

= V(C1  C2  C3)

Capacitors in Series and Parallel Class 12 Notes | EduRev 
Capacitors in Series and Parallel Class 12 Notes | EduRev

Ceq = C1  C2  C3

In general

Capacitors in Series and Parallel Class 12 Notes | EduRev

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