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  • A parallel plate capacitor is formed by two plates each of area <img alt="\mathrm{30\pi \, cm^{2}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B30%5Cpi%20%5C%2C%20cm%5E%7B2%7D%

A parallel plate capacitor is formed by two plates each of area \mathrm{30\pi \, cm^{2}} seperated by \mathrm{1\, mm}.
A material of dielectric strength \mathrm{3.6\times 10^{7}\, Vm^{-1}} is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is \mathrm{7\times 10^{-6}\, C}, the value of dielectric constant of the material is :
 \mathrm{\left [ Use \, \frac{1}{4\pi \epsilon _{0}}= 9\times 10^{9}\, Nm^{2}C^{-2} \right ]}

Option: 1

\mathrm{1.66}


Option: 2

\mathrm{1.75}


Option: 3

\mathrm{2.25}


Option: 4

\mathrm{2.33}


Answers (1)

best_answer

\mathrm{A= 30\, \pi \, cm^{2}= 30\, \pi \times 10^{-4}m^{2}}
\mathrm{d= 1\, mm= 10^{-3}m}
\mathrm{E=\text{Dielectric field strength}= 3.6\times 10^{7}\left ( \frac{V}{m} \right )}
\mathrm{Q_{max}=7\times 10^{-6}C}
\mathrm{E= \frac{\sigma }{\xi _{0}\, k}= \frac{Q}{A\, \xi _{0}\, k}}
\mathrm{3.6\times 10^{7}= \frac{7\times 10^{-6}}{30\, \pi \times 10^{-4}\times\frac{10^{-9}k}{4\, \pi\, \times 9}} }

\mathrm{\left ( \frac{1}{4\, \pi \, \xi _{0}}= 9\times 10^{9} \; \Rightarrow \; \xi _{0}= \frac{1}{4\, \pi\times 9\times 10^{9}}\right ) }

\mathrm{k= \frac{14\times 9}{15\times 3.6}= \frac{126}{15\times 3.6} }
\mathrm{k= 2.33 }

The correct option is (4)

Posted by

Ajit Kumar Dubey

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