The work done in increasing the potential of a capacitor from V volt to 2V volt is W. Then, the work done in increasing the potential of the same capacitor from 2V volt to 4V volt will be
A
W
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B
2W
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C
4W
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D
8W
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Solution
The correct option is C4W Let us try to understand this problem in two cases:
Case 1:
When the potential is changing from V to 2V
Then the work done we know is given by W.D1=Uf−Ui ⟹W.D1=12C(2V)2−12CV2 ∴W.D1=32CV2 = W......(i)
Case 2:
When the potential of the same capacitor further changes from 2V to 4V W.D2=12C(4V)2−12C(2V)2 ⟹W.D2=122CV2=6CV2.......(ii)
Comparing (i) & (ii) we get ∴W.D2 = 4W