Capacitors

JEE Main level, single correct, medium

77 of 180

Question 77 of 180

A capacitor has air as dielectric medium and two conducting plates of area 12 cm212 \mathrm{~cm}^2 and they are 0.6 cm0.6 \mathrm{~cm} apart. When a slab of dielectric having area 12 cm212 \mathrm{~cm}^2 and 0.6 cm0.6 \mathrm{~cm} thickness is inserted between the plates, one of the conducting plates has to be moved by 0.2 cm0.2 \mathrm{~cm} to keep the capacitance same as in previous case. The dielectric constant of the slab is : (Given ϵ0=8.834×10−12 F/m\epsilon_0=8.834 \times 10^{-12} \mathrm{~F} / \mathrm{m} )

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Answer: (D) 1.501.50

Aεod=Aεo(0.2+dk)0.6=0.2+0.6kk=32\begin{aligned} & \frac{\mathrm{A} \varepsilon_{\mathrm{o}}}{\mathrm{d}}=\frac{\mathrm{A} \varepsilon_{\mathrm{o}}}{\left(0.2+\frac{\mathrm{d}}{\mathrm{k}}\right)} \\ & 0.6=0.2+\frac{0.6}{\mathrm{k}} \\ & \mathrm{k}=\frac{3}{2}\end{aligned}

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