Question

The capacitance of a parallel plate capacitor with air as medium is $6\, \mu F$. With the introduction of a dielectric medium, the capacitance becomes 30 $\mu F.$ The permittivity of the medium is : $(\epsilon_0 = 8.85 \times 10^{-12} C^2N^{-1}m^{-2}$)

• A. $0.44 \times 10^{-13} C^2 N^{-1}m^{-2}$
• B. $1.77 \times 10^{-12} C^2 N^{-1}m^{-2}$
• C. $0.44 \times 10^{-10} C^2 N^{-1}m^{-2}$
• D. $5.00 \,C^2 N^{-1}m^{-2}$

Answer 1

The Correct Option is A

The correct option is(A): \(0.44 \times 10^{-13} C^2 N^{-1}m^{-2}\).

\(C=KC_{0}\)
\(K=\frac{C}{C_{0}}\)
\(=\frac{30}{6}=5\)
\(K=\frac{\varepsilon}{\varepsilon_{0}}\)
\(\varepsilon=K\,\varepsilon_{0}\)
\(=5 \times 8.85\times 10^{-12}\)
\(=0.44 \times 10^{-10}\,C^{2}\,N^{-1}\,m^{-2}\)