MHT-CET : Physics Entrance Exam

### MHT - CET : Physics - Electrostatics Page 3

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15.

Energy Stored in a Charged Condenser

Work done in depositing charge dq

dw =

v dq

=

 q C

dq

(\ C=q/v)

\ To charge the condenser fully, total work done

W =

dq =

 1 2

 Q2 C

\ The energy stored in the charged condenser

W =

 CV2 2

=

 QV 2

=

 Q2 2C

 where C: Capacitance Q: Charge the condenser V: Potential difference across condenser

16.

Combination of Condensers

Series Combination

Consider a series combination of 3 condensers C1, C2, C3 with potential difference across each of them V1, V2, V3 respectively.

If total potential difference, = V,
Then V = V1 + V2 + V3

C =

 Q V

Þ V =

 Q C

\

 Q C

=

 Q C1

+

 Q C2

+

 Q C3

 1 C

=

 1 C1

+

 1 C2

+

 1 C3

In general, for a series combination of
n condensers of capacities C1, C2, … , Cn, the effective capacitance

 1 C

=

Parallel combination

 In a parallel combination of condensers (of capacities C1, C2, C3) the potential difference across them is the same. The total charge of the combination is the sum of the charges on the individual condensers.

Q = Q1 + Q2 + Q3

 But Q = CV    \ CV = C1V + C2V + C3V \ C = C1 + C2 + C3

The resultant capacitance is equal to the sum of their individual capacities.

In general, for a parallel combination of
n condensers of capacities C1, C2,…, Cn the equivalent capacity

 C =

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