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Two capacitors, each of capacitance 40 μ F, are connected in series. The space inside one of them is then filled with a dielectric material of dielectric constant K, so that the equivalent capacitance of the system becomes 24 μ F. The value of K will be

Asked in JEE Main 28th July 1st Shift 2022 · Dielectric slab

• (1) 1.5
• (2) 2.5
• (3) 1.2
• (4) 3

Step-by-step solution

Why the other options are wrong

• (2) Solves (40K)/(K+1)=24 as 40K=24K+40, dropping the K inside the bracket on the right.
• (3) Comes from (24)/(20), i.e. taking the ratio of the new equivalent capacitance to the old one 20 μ F; that ratio is not K, because only one capacitor changes.
• (4) Would give (40×3)/4=30 μ F, not 24 μ F; it comes from equating K to (C_eq)/8.

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