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Question

A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage V) as ε=αV where α=2V1. A similar capacitor with no dielectric is charged to V0=78V. It is then connected to the uncharged capacitor with the dielectric. Final voltage on the capacitor is

A
2V
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B
3V
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C
5V
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D
6V
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Solution

The correct option is D 6V
On connecting the two given capacitors, let the final voltage be V.
If capacity of capacitor without the dielectric is C, then the charge on this capacitor is q1=CV
The other capacitor with dielectric has capacity εC.
Therefore, charge on it is q2=εCV
As ε=αV, therefore q2=ε=αV
The initial charge on the capacitor (Without dielectric)
that was charged is q0=CV0
From the conservation of charge, q0=q1+q2
CV0=CV+αCV2orV2+VV0=0
V=1±1+4αV02α
using α=2V1 or V0=78V, we get
V=1±1+(4×2×78)2×2=1±6254
As V is positive, therefore, V=62514=244=6V,

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