Show that the energy stored by a series combination of capacitors is the same as that in the parallel combination.

Asked by nilesh gangwani | 29th 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) qC2 +(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.
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Team
Topperlearning

Answered by  | 29th Nov, 2010, 11:33: AM

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