A parallel plate air capacitor, with plate separation ' d ' has a capacitance of 9 pF. The space between the plates is now filled with two dielectrics, the first having K₁ = 3 and thickness d₁ = d/3, while the 2 nd has K₂ = 6 and thickness d₂ = 2d/3. The capacitance of the new capacitor is: (a) 3.8 pF (b) 20.25 pF (c) 40.5 pF (d) 45 pF

Answer: (c). Layers in series: C=(ε₀A)/(d/3/3+2d/3/6)=(ε₀A)/(2d/9)=4.5C₀ C=4.5×9=40.5 pF So the answer is (c) 40.5 pF.

A parallel plate air capacitor, with plate separation ' d ' has a… | MHT CET 2024 (4 May, Shift 1)

Q44MHT CET 2024 · 4 MAY · SHIFT 1Medium

Dielectrics

A parallel plate air capacitor, with plate separation ' d ' has a capacitance of 9 pF. The space between the plates is now filled with two dielectrics, the first having $K_1 = 3$ and thickness $d_1 = d/3$ , while the $2$ nd has $K_2 = 6$ and thickness $d_2 = 2d/3$ . The capacitance of the new capacitor is:

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Answer: (c)

Layers in series: $C=\frac{\epsilon_0A}{\frac{d/3}{3}+\frac{2d/3}{6}}=\frac{\epsilon_0A}{\frac{2d}{9}}=4.5C_0$
$C=4.5\times9=40.5\text{ pF}$
So the answer is (c) 40.5 pF.

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Dielectrics question from MHT CET 2024 (4 May, Shift 1)

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