A parallel plate capacitor has plate area 40 cm² and plates separation 2 mm. The space between the plates is filled with a dielectric medium of a thickness 1mm and dielectric constant 5. The capacitance of the system is :

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$24 ε_{0} F$

$\frac{3}{10} ε_{0} F$

$10 ε_{0} F$

$\frac{10}{3} ε_{0} F$

answer is A.

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Detailed Solution

$\begin{array}{l} A = 40 \times 10^{- 4} m^{2} = 4 \times 10^{- 3} m^{2} \\ d = 2 \times 10^{- 3} m \cdot k = 5, t = 10^{- 3} m, C = ? \\ C = \frac{ϵ_{0} A}{d - t + \frac{t}{k}} = \frac{ϵ_{0} \times 4 \times 10^{- 3}}{(2 - 1) \times 10^{- 3} + \frac{10^{- 3}}{5}} = \frac{4 ϵ_{0} \times 5}{6} = \frac{10 ϵ_{0}}{3} F \end{array}$