How to find relative permittivity from R, C and ρ?

εᵣ=RC/(ε₀ρ)=17.7×10¹⁴×10⁻⁶/(8.85×10⁻¹²×10¹³)=2×10⁷. So α=2.

What is the product RC for a parallel plate capacitor?

RC=ε₀εᵣρ. The plate area and separation cancel in the product.

Parallel plate capacitor d=0.885mm C=1μF resistivity 10¹³Ωm resistance 17.7×10¹⁴Ω — relative permittivity

JEERANKERS

PhysicsElectrostatics

QInteger TypeCapacitors

A parallel plate capacitor has separation 0.885 mm, capacitance 1 μF. Filled with material of resistivity $10^{13}$ Ωm and resistance $17.7\times10^{14}$ Ω. Relative permittivity $\varepsilon_r=\alpha\times10^7$. Find $\alpha$. ($\varepsilon_0=8.85\times10^{-12}$ F/m)

✅ Correct Answer

α = 2

✓

Solution

Use the key relation RC = ε₀εᵣρ

$R=\dfrac{\rho d}{A},\quad C=\dfrac{\varepsilon_0\varepsilon_r A}{d}$

Product: $RC=\varepsilon_0\varepsilon_r\rho$ (geometry cancels)

Solve for εᵣ

$\varepsilon_r=\dfrac{RC}{\varepsilon_0\rho}=\dfrac{17.7\times10^{14}\times10^{-6}}{8.85\times10^{-12}\times10^{13}}=\dfrac{17.7\times10^{8}}{8.85\times10^{1}}=2\times10^{7}$

$\alpha=\boxed{2}$

📘 RC = ε₀εᵣρ for Leaky Capacitor

$R=\rho d/A$ and $C=\varepsilon_0\varepsilon_r A/d$. Product $RC=\varepsilon_0\varepsilon_r\rho$ — geometry cancels. This gives $\varepsilon_r$ directly.

💡

Important Concepts

RC=ε₀εᵣρ DerivationR=ρd/A and C=ε₀εᵣA/d. RC=(ρd/A)(ε₀εᵣA/d)=ε₀εᵣρ. Both d and A cancel completely.

CalculationRC=17.7×10¹⁴×10⁻⁶=17.7×10⁸. ε₀ρ=8.85×10⁻¹²×10¹³=88.5. εᵣ=17.7×10⁸/88.5=2×10⁷.

Physical MeaningRC=ε₀εᵣρ is the dielectric relaxation time — time for charge to redistribute in the medium.

Answerεᵣ=2×10⁷, so α=2.

FAQs

What is the RC product formula?

⌄

RC=ε₀εᵣρ. This is derived from R=ρd/A and C=ε₀εᵣA/d — the plate area and separation cancel.

Numerical steps?

⌄

RC=17.7e14×1e-6=17.7e8. ε₀ρ=8.85e-12×1e13=88.5. εᵣ=17.7e8/88.5=2e7.

Why is εᵣ so large?

⌄

This is a theoretical exercise — real dielectrics have εᵣ typically 2-100.

What would be the time constant τ=RC?

⌄

τ=RC=ε₀εᵣρ=8.85×10⁻¹²×2×10⁷×10¹³=1.77×10⁹ s ≈ 56 years.

Is this from JEE Main 2026?

⌄

Yes, this appeared in JEE Main 2026 Section B.

🔗