JEE Main 2026 Apr 8 Shift 2, Physics Q21: Capacitors And Capacitance

JEE Main2026Apr 8, Shift 2Physics

A parallel plate capacitor is having separation between plates $0.885$ mm. It has a capacitance of $1 μ$ F when the space between the plates is filled with an insulating material of resistivity $1 \times 1 0^{13} Ω \cdot$ m and resistance $17.7 \times 1 0^{14} Ω$ . Relative permittivity of the insulating material is $α \times 1 0^{7}$ . The value of $α$ is _________. (Take permittivity of free space $= 8.85 \times 1 0^{- 12}$ F/m)

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Solution

For a parallel-plate capacitor filled with the same dielectric of resistivity $ρ$ and relative permittivity $K$ , the product $R C$ is geometry-independent:

$R C = \frac{ρ d}{A} \cdot \frac{K ϵ _{0} A}{d} = ρ K ϵ_{0}$

Solving for $K$ :

$K = \frac{R C}{ρ ϵ _{0}} = \frac{( 17.7 \times 1 0 ^{14} ) ( 1 \times 1 0 ^{- 6} )}{( 1 \times 1 0 ^{13} ) ( 8.85 \times 1 0 ^{- 12} )}$

$= \frac{17.7 \times 1 0 ^{8}}{8.85 \times 1 0 ^{1}} = \frac{17.7}{8.85} \times 1 0^{7} = 2 \times 1 0^{7}$ .

$∴$ $α = 2$ .

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JEE Main 2026 Apr 8 Shift 2, Physics Q21: Capacitors And Capacitance

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