A parallel plate condenser with oil between the plates (dielectric constant of oil K = 2) has a capacitance C. If the oil is removed, then capacitance of the capacitor becomes

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AIIMS BSc NURSING 2024 Memory-Based Paper

Answer 1

Concept:

Capacitance of a Parallel Plate Capacitor:

The capacitance C of a parallel plate capacitor with a dielectric material between the plates is given by the formula:
C = (K × ε₀ × A) / d, where:
- K = Dielectric constant of the material (dimensionless)
- ε₀ = Permittivity of free space (8.85 × 10⁻¹² F/m)
- A = Area of the plates (m²)
- d = Distance between the plates (m)
When a dielectric material (oil) is inserted between the plates, the capacitance increases by a factor of K (dielectric constant).
If the oil is removed (K = 1 for air or vacuum), the capacitance will be reduced by a factor of K.

Calculation:

Initially, the capacitance is C = K × C₀, where C₀ is the capacitance without the oil.

Given that K = 2 with the oil, the capacitance becomes C = 2 × C₀.

When the oil is removed (K = 1), the capacitance reduces to:

C' = C / K = 2C / 2 = C / 2

∴ The capacitance of the capacitor becomes C / 2, which corresponds to Option 4.