A parallel plate capacitor has plate area and plate separation 2 mm. The space between the plates is filled with a dielectric medium of thickness 1 mm and dielectric constant 5. The capacitance of the system is [2023]

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Solution

Q.
A parallel plate capacitor has plate area $40 {cm}^{2}$ and plate separation 2 mm. The space between the plates is filled with a dielectric medium of thickness 1 mm and dielectric constant 5. The capacitance of the system is [2023]

1 $\frac{10}{3} ε_{0} F$

2 $\frac{3}{10} ε_{0} F$

3 $24 ε_{0} F$

4 $10 ε_{0} F$

Ans.
(1)

$A = 40 \times 10^{- 4} m^{2} = 4 \times 10^{- 3} m^{2}$

$d = 2 \times 10^{- 3} m, k = 5, t = 10^{- 3} m, C = ?$

$C = \frac{ε_{0} A}{d - t + \frac{t}{k}}$ $= \frac{ε_{0} \times 4 \times 10^{- 3}}{(2 - 1) \times 10^{- 3} + \frac{10^{- 3}}{5}}$ $= \frac{4 ε_{0} \times 5}{6} = \frac{10 ε_{0}}{3} F$

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