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

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