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Home » The distance between the plates of a parallel plate capacitor is d. A metal plate of thickness is placed between the plates. What will be the effect on the capacitance?
The distance between the plates of a parallel plate capacitor is d. A metal plate of thickness \left(\frac{d}{2}\right) is placed between the plates. What will be the effect on the capacitance?
Physics | Previous Year Question Papers
The distance between the plates of a parallel plate capacitor is d. A metal plate of thickness \left(\frac{d}{2}\right) is placed between the plates. What will be the effect on the capacitance?

Ans: For air C_{0}=\frac{A \in_{0}}{d}
Thickness t=\frac{d}{2} only when k=\infty

    \[\begin{array}{l} C_{0}=\frac{A \in_{0}}{d} \\ C_{\text {mat }}=\frac{A \in_{0}}{(d-t)} \end{array}\]

    \[\begin{array}{l} \Rightarrow \mathrm{C}_{\text {menal }}=\frac{\mathrm{A} \epsilon_{0}}{\left(\mathrm{~d}-\frac{\mathrm{d}}{2}\right)} \\ \Rightarrow \mathrm{C}_{\text {meval }}=2 \mathrm{~A} \epsilon_{0} \\ \Rightarrow \mathrm{C}_{\text {meal }}=2 \mathrm{C}_{0} \end{array}\]

Hence, capacitance will double.

i

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