In a parallel plate capacitor set up, the plate area of capacitor is 2 m 2 and the plates are separated by 1 m . If the space between the plates are filled with a dielectric material of thickness 0 .

Question

In a parallel plate capacitor set up, the plate area of capacitor is $2 m^{2}$ and the plates are separated by $1 m$ . If the space between the plates are filled with a dielectric material of thickness $0.5 m$ and are $2 m^{2}$ (see figure) the capacitance of the set-up will be $ε_{0}$ ________.

(Dielectric constant of the material $= 3.2$ )

(Round off to the Nearest Integer)

TestHub · Accepted Answer

The given system can be considered as a series combination of two capacitors. The equivalent capacitance can be given as,

$\frac{1}{C} = \frac{1}{C_{1}} + \frac{1}{C_{2}} \Rightarrow \frac{1}{C} = \frac{\frac{d}{2}}{K ε_{0} A} + \frac{\frac{d}{2}}{ε_{0} A}$

$\Rightarrow C = \frac{ε_{0} A}{\frac{d}{2 K} + \frac{d}{2}} = \frac{2 ε_{0} A}{\frac{d}{K} + d}$

$= \frac{2 \times 2 ε_{0}}{\frac{1}{3.2} + 1} = \frac{4 \times 3.2}{4.2} ε_{0}$

$= 3.04 ε_{0}$

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