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  • The capacitance of a parallel plate capacitor with air as a medium is  With the introduction of a dielectric medium, the capacitance becomes <img alt="

The capacitance of a parallel plate capacitor with air as a medium is 6 \mu F With the introduction of a dielectric medium, the capacitance becomes 30 \mu F . The permittivity of the medium is: \left(\varepsilon_0 = 8.875\times 10^{-12}C^2N^{-1}m^{-2} \right )
Option: 1 0.44\times 10^{-12} C^2N^{-1}m^{-2}
Option: 2 1.77\times 10^{-12} C^2N^{-1}m^{-2}
Option: 3 0.44\times 10^{-10} C^2N^{-1}m^{-2}
Option: 4 500\ C^2N^{-1}m^{-2}

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\\ \text{Capacitance of air capacitor} \ C_{0}=\frac{\varepsilon_{0} A}{d}=6 \mu F$ \\ \\ When a dielectric of permittivity $\varepsilon_{ r }$ and dielectric constant $K$ is introduced between the plates, then capacitance, \\\\ $C =\frac{ K \varepsilon_{0} A }{ d }=30 \mu F$ \\\\ Dividing eq. (ii) by (i), \\ we get $\frac{ C }{ C _{0}}=\frac{\frac{ K \epsilon_{0} A }{ d }}{\frac{\varepsilon_{0} A }{ d }}=\frac{30}{6}$ \\ \\ $\Rightarrow K =5$ \\ \\ $\therefore$ permittivity of the medium \\ \\ $\varepsilon_{0}=\varepsilon_{0} K$ $=8.85 \times 10^{-12} \times 5=0.44 \times 10^{-10}

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