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 plates but thicknes

Question

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 plates but thickness d 2 is inserted between the plates. Capacitance of the capacitor in the presence of slab will be ______ µ F .

TestHub · Accepted Answer

Capacitance of the parallel plate capacitor when air is present $C = \frac{ϵ_{0} A}{d} = 5 μF$

After insertion of dielectric, the equivalent capacitance of the new capacitor is

$C_{eq} = \frac{ϵ_{0} A}{\frac{\frac{d}{2}}{1.5} + \frac{\frac{d}{2}}{1}}$

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

$= \frac{6}{5} \times 5 μF = 6 μF$ .

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