In a parallel plate capacitor of capacitance C, a metal sheet is inserted between the plates parallel to them. If the thickness of the sheet is one third of the separation between the plates, the capacitance of the capacitor will be
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \displaystyle\frac{3C}{2} \)
Inside a metal sheet the electric field is zero, so the sheet simply removes its own thickness \( t \) from the gap. The capacitor behaves as one with plate separation \( d - t \).
\( \displaystyle C = \frac{\varepsilon_0 A}{d} \qquad C' = \frac{\varepsilon_0 A}{d - t} \)
Putting \( t = d/3 \):
\( \displaystyle C' = \frac{\varepsilon_0 A}{d - d/3} = \frac{\varepsilon_0 A}{2d/3} = \frac{3}{2}\,\frac{\varepsilon_0 A}{d} = \frac{3C}{2} \)