# In a parallel plate capcitor set up, the plate area of capacitor is 2m2 and the plates are separated by 1m. If the space between the plates are filled with a dielectric material of thickness 0.5m and area 2m2 (see fig) the capacities of the set-up will be _____ . (Dielectric constant of material =3.2)  (rounded off to the nearest integer) Option: 1 3 Option: 2 4 Option: 3 5 Option: 4 6

\begin{aligned} C &=\frac{\varepsilon_{0} A}{\frac{d}{2 K}+\frac{d}{2}}=\frac{2 \varepsilon_{0} A}{\frac{d}{K}+d} \\ &=\frac{2 \times 2 \varepsilon_{0}}{\frac{1}{3.2}+1}=\frac{4 \times 3.2}{4.2} \varepsilon_{0} \\ &=3.04 \varepsilon_{0}\approx 3 \varepsilon_{0} \end{aligned}

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