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

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

AFMCAFMC 2004

Solution:

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