The capacitance of a parallel plate capacitor with air as medium is 3 μ F . With the introduction of a dielectric medium between the plates, the capacitance becomes 15 μ F . The permittivity of the medium is

Question

The capacitance of a parallel plate capacitor with air as medium is 3 μ F . With the introduction of a dielectric medium between the plates, the capacitance becomes 15 μ F . The permittivity of the medium is (A) 5 C 2 N -1 m -2 (B) 15 C 2 N -1 m -2 (C) 0.44 × 10-10 C 2 N -1 m -2 (D) 8.845 × 10-11 C 2 N -1 m -2

Tardigrade Admin · Accepted Answer

Capacitance of a parallel plate capacitor with air is

C = \frac{ε _{0} A}{d}

Capacitance of a same parallel plate capacitor with the introductory of a dielectric medium

C^{^{'}} = \frac{k ε _{0} A}{d}

where

k

is the dielectric constant of a medium.

∴ \frac{C ^{^{'}}}{C} = k \to= \frac{15}{3} = 5

and

k = \frac{ε}{ε _{0}}

or

ε = k ε_{0} = 5 \times 8.854 \times 1 0^{- 12}

= 0.4427 \times 1 0^{- 10} C^{2} N^{- 1} m^{- 2}

Q. The capacitance of a parallel plate capacitor with air as medium is $3 μ F$ . With the introduction of a dielectric medium between the plates, the capacitance becomes $15 μ F$ . The permittivity of the medium is

$5 C^{2} N^{- 1} m^{- 2}$

$15 C^{2} N^{- 1} m^{- 2}$

$0.44 \times 1 0^{- 10} C^{2} N^{- 1} m^{- 2}$

$8.845 \times 1 0^{- 11} C^{2} N^{- 1} m^{- 2}$

Q. The capacitance of a parallel plate capacitor with air as medium is 3μF . With the introduction of a dielectric medium between the plates, the capacitance becomes 15μF . The permittivity of the medium is

5C2N−1m−2

15C2N−1m−2

0.44×10−10C2N−1m−2

8.845×10−11C2N−1m−2

Q. The capacitance of a parallel plate capacitor with air as medium is $3 μ F$ . With the introduction of a dielectric medium between the plates, the capacitance becomes $15 μ F$ . The permittivity of the medium is

$5 C^{2} N^{- 1} m^{- 2}$

$15 C^{2} N^{- 1} m^{- 2}$

$0.44 \times 1 0^{- 10} C^{2} N^{- 1} m^{- 2}$

$8.845 \times 1 0^{- 11} C^{2} N^{- 1} m^{- 2}$