CBSE 2025, Set 1

Question

A metal sheet is inserted between the plates of a parallel plate capacitor of capacitance C. If the sheet partly occupies the space between the plates, the capacitance : A). remains C B). becomes greater than C C). becomes less than C D). becomes zero

Edvaya · Accepted Answer

The correct answer is becomes greater than C. When a metal sheet (conductor) is inserted between the plates of a parallel plate capacitor, it is equivalent to reducing the effective separation between the plates. If the metal sheet of thickness $t$ is inserted, the effective gap reduces from $d$ to $(d - t)$, giving: $$C' = \frac{\varepsilon_0 A}{d - t} > \frac{\varepsilon_0 A}{d} = C$$ Even if the sheet only **partly** occupies the space between the plates, the effective separation is still reduced over that partial region. Treating the capacitor as two capacitors in parallel — one region with the sheet (higher capacitance) and one without — gives a net capacitance **greater than C**. > **Key tip:** A conductor inserted between capacitor plates always increases capacitance. A dielectric also increases it (by factor K). The capacitance becomes zero only if the sheet touches both plates (short circuit), which is not the case here.

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Physics > Electrostatics And Current Electricity > Electrostatic Potential And Capacitance

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