A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (V) as 
where 
. A similar capacitor with no dielectric is charged to 
. It is then connected to the uncharged capacitor with the dielectric. Final voltage on the capacitor is.
Text Solution
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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 
the other capacitor with dielectric has capacity 
.
Therefore , charge on it is 
As 
therefore, 
The initial charge on the capacitor (without dielectric) that was charged is
Form the conservation of charge,
or 
Using 
and 
we get
As V is positive, therefore, 
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