Question

A thin aluminium sheet is placed between the plates of a parallel plate capacitor. Its capacitance will:

• A. increase
• B. decrease
• C. remain same
• D. become infinite

Answer 1

Answer: (C)

On inserting a thin aluminium sheet between the plates of a capacitor it act as two capacitors connected in series.
The combination shows two capacitor connected in series. Resultant capacitance is

$\frac{1}{C^{\prime }}=\frac{1}{C_1}+\frac{1}{C_2}$
$C=\frac{K{\epsilon }_{0}A}{d}$
where, $A$ is area, $d$ is the distance between the plates and $K$ is dielectric constant $(=1)$.
Therefore, $C_1=\frac{{\epsilon }_{0}A}{d/2},C_2=\frac{{\epsilon }_{0}A}{d/2}$
$\therefore \frac{1}{C^{\prime }}=\frac{d/2}{{\epsilon }_{0}A}$
$\frac{1}{C^{\prime }}=\frac{d}{{\epsilon }_{0}A}$
$\Rightarrow C^{\prime }=\frac{{\epsilon }_{0}A}{d}=C$
Hence, on inserting aluminium sheet the capacitance remains the same.