CBSE Class 12-science Answered
Show that the energy stored by a series combination of capacitors is the same as that in the parallel combination.
Asked by nilesh gangwani | 29 Nov, 2010, 10:44: AM
Expert Answer
Dear student
Energy stored in a series combination of capacitors
Let q be the charge given to a group of capacitors of capacities C1 , C2 , C3 resp. connected in series with each othet. Since they are in series each will get charged with the charge q. If C is the net capacity of the combination,
1/C = 1/ C1 + 1 / C2 + 1/ C3
Total energy W stored in the combination is
W = (1/2) (q2 / C) = (1/2) q2 [1/ C1 + 1 / C2 + 1/ C3 ] = (1/2) q2 C1 +(1/2) q2 C2 +(1/2) q2 C3
or, W = W1 + W2 + W3
Energy stored in a parallel combination of capacitors:
When a no. of capacitors having capacities C1 , C2 , C3 resp. are connected in parallel, they get charged to same potential V. If C is the net capacity of combination, then
C = C1 + C2 + C3
Total energy, stored in the combination is:
W = (1/2) ( CV2 )
or, W = (1/2)( C1 + C2 + C3 )V2
or, W = W1 + W2 + W3
Therefore,
Net energy stored in a combination of capacitors is equal to the sum of energies stored in the component capacitors whatever type of combination it be:series, parallel or grouping.
We hope this clarifies your doubt.
Regards
Team
Topperlearning
Answered by | 29 Nov, 2010, 11:33: AM
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