question_answer

A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor [AIEEE 2003]

A) decreases

B) remains unchanged

C) becomes' infinite

D) increases

Correct Answer: A

Solution :

[b] Aluminium is a metal, so when we insert an aluminium foil, equal and opposite charges appear on its two surfaces. Since, it is of negligible thickness, it will not effect the capacitance.

Alternative Solution

From the formula,

\[C=\frac{{{\varepsilon }_{0}}A}{d-t+\frac{t}{K}}\]

Here, \[K=\infty \] and \[t\to 0\]

So,       \[C=\frac{{{\varepsilon }_{0}}A}{d+0}=\frac{{{\varepsilon }_{0}}A}{d}={{C}_{0}}\]