A parallel-plate capacitor stores q = 10 μC at V = 1000 V. With air dielectric, its minimum plate area is A₁. With dielectric constant K = 3, and breakdown field eight times that of air, its minimum area is A₂. If A₁/A₂ = 8k, find k.
Physics · Mixed Chapter
JEE Main Practice

Question

A parallel-plate capacitor stores q = 10 μC at V = 1000 V. With air dielectric, its minimum plate area is A₁. With dielectric constant K = 3, and breakdown field eight times that of air, its minimum area is A₂. If A₁/A₂ = 8k, find k.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — C = Kε₀A/d and E = V/d. At safe maximum Eₘₐₓ, minimum allowed separation is dₘᵢₙ = V/Eₘₐₓ. Step 2 — For fixed q and V, C = q/V and hence Aₘᵢₙ = q/(Kε₀Eₘₐₓ). Step 3 — For dielectric, K increases from 1 to 3 and breakdown field increases 8 times; A₁/A₂ = 3 × 8 = 24. Step 4 — Since A₁/A₂ = 8k, k = 24/8 = 3.