Air capacitor has capacitance ' C₁ '. The space between two plates of capacitor is filled with two dielectrics as shown in figure. The new capacitance of the capacitor is ' C₂ '. The ratio (C₁)/(C₂) is (d = distance between two plates of capacitor, K₁ and K₂ are dielectric constants of two dielectrics respectively) (a) K₁ + K₂ (b) (K₁+K₂)/(K₁-K₂) (c) (2K₁K₂)/(K₁+K₂) (d) (K₁+K₂)/(2K₁K₂)

Answer: (d). The two dielectrics fill the gap one after the other, each d/2 thick: series. C₂=(ε₀A)/(d/2K₁+d/2K₂)=C₁·(2K₁K₂)/(K₁+K₂) (C₁)/(C₂)=(K₁+K₂)/(2K₁K₂). So the answer is (d).

Air capacitor has capacitance ' C₁ '. The space between two plates of… | MHT CET 2024 (16 May, Shift 2)

Q42MHT CET 2024 · 16 MAY · SHIFT 2Medium

Dielectrics

Air capacitor has capacitance ' $C_1$ '. The space between two plates of capacitor is filled with two dielectrics as shown in figure. The new capacitance of the capacitor is ' $C_2$ '. The ratio $\frac{C_1}{C_2}$ is $(d =$ distance between two plates of capacitor, $K_1$ and $K_2$ are dielectric constants of two dielectrics respectively)

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Answer: (d)

The two dielectrics fill the gap one after the other, each $\frac{d}{2}$ thick: series.
$C_2=\frac{\epsilon_0A}{\frac{d}{2K_1}+\frac{d}{2K_2}}=C_1\cdot\frac{2K_1K_2}{K_1+K_2}$
$\frac{C_1}{C_2}=\frac{K_1+K_2}{2K_1K_2}$ . So the answer is (d).

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Dielectrics question from MHT CET 2024 (16 May, Shift 2)

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