Question

A parallel plate capacitor with air between the plates has capacitance 9 pF. The separation between the plates becomes thrice and the space between them is filled with a medium of dielectric constant 6. The capacitance becomes 'x' pF. The value of 'x' is ______.

विकल्प

• 9

• 18

• 4.5

• 27

Answer 1

A parallel plate capacitor with air between the plates has capacitance 9 pF. The separation between the plates becomes thrice and the space between them is filled with a medium of dielectric constant 6. The capacitance becomes 'x' pF. The value of 'x' is 18.

Explanation:

\[\mathrm{C}=\frac{\varepsilon_0\mathrm{A}}{\mathrm{d}}=9\mathrm{pF}\] and \[\mathrm{C^{\prime}}=\frac{\varepsilon_0\mathrm{kA^{\prime}}}{\mathrm{d^{\prime}}}\]

But \[\mathrm{A^{\prime}=A~,d^{\prime}=3d,}\]

\[\therefore\quad\mathrm{C^{\prime}}=\frac{\varepsilon_0\mathrm{k}\times\mathrm{A}}{3\mathrm{d}}=\frac{6\times\varepsilon_0\mathrm{A}}{3\mathrm{d}}\]

\[\therefore\quad\mathrm{C^{\prime}}=2\times9\mathrm{pF}=18\mathrm{pF}\]