Assertion : A parallel plate capacitor is connected across batter… - Vidyadip

MCQ

Assertion : A parallel plate capacitor is connected across battery through a key. A dielectric slab of dielectric constant $K$ is introduced between the plates. The energy which is stored becomes $K$ times.

Reason : The surface density of charge onthe plate remains constant or unchanged.

A
If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
B
If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
✓
If the Assertion is correct but Reason is incorrect.
D
If both the Assertion and Reason are incorrect.

✓

Answer

Correct option: C.

If the Assertion is correct but Reason is incorrect.

c
In the given cases, $\mathrm{V}=\mathrm{V}_{0}$ (remains constant).

Energy stored inthe capacitor $\mathrm{U}=\frac{1}{2} \mathrm{CV}^{2}$

When a dielectric slab of dielectric constant

$\mathrm{K}$ is introduced between the plates of the

condenser, then $\mathrm{C} \longrightarrow \mathrm{KC}$

So energy stored will become $K$ times.

since $Q=C V,$ So $Q$ will become $K$ times

$\therefore $ Surface charge density

$\sigma^{\prime}=\frac{\mathrm{KQ}}{\mathrm{A}}=\mathrm{K} \sigma_{0}$

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