Assertion: A parallel plate capacitor is connected across battery through a key. A dielectric slab of constant `K` is introduced between the plates. The energy which is stored becomes`K` times.
Reason: The surface density of charge on the plate remains constant or uncharged

Options

A. If both assertion and reason are true and reson is the correct explanation of the assertion.
B. If both assertion and reason are true but reason is not the correct explanation of the assertion.
C. If the assertion is true but the reason are false.
D. If both the assertion and reason are false.

Answer

C

Explanation

If a dielectric slab of dielectric constant `K` is filled in between the plates of a condenser while charging it, the potential difference between the plates does not chartge but the capacity `K` times, therefore `V' = V, C' = KC`.
`:.` Energy stored in the capacity
`U' = (1)/(2)C'V'^(2)`
`= (1)/(2)(CV)(V^(2))`
`= [(1)/(2) CV^(2)] K = KU`
Thus, energy stored becomes `K` times.
Surface charge density
`sigma' = (q')/(A) = (C'V')/(A) = (KCV)/(A) = K(q)/(A) = K sigma`