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A parallel plate capacitor is having separation between plates 0.885 mm. It has a capacitance of 1 μF when the space between the plates is filled with an insulating material of resistivity 1×10¹³ Ω m and resistance 17.7×10¹⁴ Ω. Relative permittivity of the insulating material is α×10⁷. The value of α is ______. (Take permittivity of free space =8.85×10⁻¹² F/m)

Asked in JEE Main 8th April 2nd Shift 2026 · Resistance of a wire and stretching

Answer: 2

Step-by-step solution

C=(Kε₀A)/d and the leakage resistance R=(ρ d)/A.

Multiplying: RC=ρ Kε₀, independent of A and d.

K=(RC)/(ρε₀)=(17.7×10¹⁴×10⁻⁶)/(10¹³×8.85×10⁻¹²).

K=(1.77×10⁹)/(88.5)=2×10⁷, so α=2.

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