A parallel plate capacitor is of area 6 cm² and separation 3 mm. The gap is filled with three dielectric slabs of equal thickness standing side by side, each spanning the full 3 mm separation, with dielectric constants K₁=10, K₂=12 and K₃=14. The dielectric constant of a single material which, when…

Question

A parallel plate capacitor is of area 6 cm² and separation 3 mm. The gap is filled with three dielectric slabs of equal thickness standing side by side, each spanning the full 3 mm separation, with dielectric constants K₁=10, K₂=12 and K₃=14. The dielectric constant of a single material which, when fully inserted in the given capacitor, gives the same capacitance would be

Accepted Answer

(2) 12. The slabs stand side by side across the full separation, so each is a capacitor of area A/3 and gap d, and the three are in parallel. C=(ε₀(A/3))/d(K₁+K₂+K₃)=(ε₀A)/d·(10+12+14)/3. (36)/3=12, so C=(12ε₀A)/d. A single slab filling the whole gap gives C=(Kε₀A)/d, so K=12. (The area and the separation never enter; only the mean of the three constants matters.)

Step-by-step solution

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