A capacitor has capacitance when its parallel plates are separated by air medium of thickness . A slab of material of dielectric constant 1.5 having area equal to that of the plates but thickness is inserted between the plates. [2023]

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Solution

Q.
A capacitor has capacitance $5 μ F$ when its parallel plates are separated by air medium of thickness $d$ . A slab of material of dielectric constant 1.5 having area equal to that of the plates but thickness $\frac{d}{2}$ is inserted between the plates. The capacitance of the capacitor in the presence of the slab will be _________ $μ F$ . [2023]

Ans.
(6)

$\frac{ε_{0} A}{d} = 5 μ F$

$C_{new} = \frac{ε_{0} A}{\frac{(\frac{d}{2})}{1.5} + \frac{(\frac{d}{2})}{1}}$

$= \frac{ε_{0} A}{(\frac{d}{3} + \frac{d}{2})} = \frac{6 ε_{0} A}{5 d} = \frac{6}{5} \times 5 μ F = 6 μ F$

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