KVPY Sample Paper KVPY Stream-SX Model Paper-31

A capacitor is filled with an insulator and a certain potential difference is applied to its plates. The energy stored in the capacitor is U. Now the capacitor is disconnected from the source and the insulator is pulled out of the capacitor. The work performed against the forces of electric field in pulling out the insulator is 4U. Then dielectric constant of the insulator is:

A) 4

B) 8

C) 5

D) 3

Correct Answer: C

Solution :

Let \[{{C}_{0}}\] be the capacity of capacitor without insulator and C its capacity with insulator. Then
\[c=k{{C}_{0}}\](k = dielectric constant) charge q remains constant.
\[\therefore \,\,\,\,\,\,\,u=\frac{1}{2}\frac{{{q}^{2}}}{c}\]	...(1)
And \[U+4U=\frac{1}{2}\frac{{{q}^{2}}}{{{c}_{0}}}\] or \[5U=\frac{1}{2}\frac{{{q}^{2}}}{{{C}_{0}}}\]		...(2)
From Equation (1) and (2), we get
\[\frac{C}{{{C}_{0}}}=5\] or k=5