A parallel plate capacitor is filled with two different dielectric slabs of equal thickness and dielectric constants and placed one on top of the other between plates of separation . What is the effective dielectric constant of the capacitor?
Answer and explanation
Correct answer: B.
- Step 1: Two dielectric slabs of thickness stacked perpendicular to the electric field lines act as two individual capacitors connected in series.
- Step 2: The individual capacitances are and .
- Step 3: In series: . Inverting gives , so the effective dielectric constant is the harmonic mean: .
Answer
.
Why not the others: is the arithmetic mean obtained when slabs divide the plate area (parallel arrangement); is the geometric mean; misses the factor of 2.
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