A parallel plate capacitor is having separation between plates 0.885 mm. It has a capacitance of 1 when the space

Question

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 $1 \times 10^{13} Ωm$ and resistance $17.7 \times 10^{14} Ω$ . Relative permittivity of the insulating material is $α \times 10^{7}$ . The value of $α$ is _______. [2026]

(Take permittivity of free space = $8.85 \times 10^{- 12} F/m$ )

Smart Achievers · Accepted Answer

(2)

$C = \frac{A ε_{0} ε_{r}}{d} \Rightarrow ε_{r} = \frac{C d}{A ε_{0}}$ $α$

$R = \frac{ρ d}{A} \Rightarrow A = \frac{ρ d}{R}$ $. . . (i i)$

$On solving eq. (i) and eq. (ii)$

$ε_{r} = (\frac{R}{ρ d}) (\frac{C d}{ε_{0}}) = \frac{R C}{ρ ε_{0}}$

$ε_{r} = \frac{17.7 \times 10^{14} \times 1 \times 10^{- 6}}{1 \times 10^{13} \times 8.85 \times 10^{- 12}} = 2 \times 10^{7}$

$\Rightarrow α = 2$

Solution

Want Us to Email you About Special Offers & Updates?

Solution

Ans. (2) C=Aε0εrd⇒εr=CdAε0 ...(i) R=ρdA⇒A=ρdR ...(ii) On solving eq. (i) and eq. (ii) εr=(Rρd)(Cdε0)=RCρε0 εr=17.7×1014×1×10-61×1013×8.85×10-12=2×107 ⇒α=2

Want Us to Email you About Special Offers & Updates?