In a parallel plate capacitor set up, the plate area of capacitor is… | JEE Main 2021 (16 Mar, Shift 2)

Q75JEE Main 2021 · 16 MAR · SHIFT 2Easy

Dielectrics

In a parallel plate capacitor set up, the plate area of capacitor is 2 m2 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 area 2 m2 (see fig.) the capacitance of the set-up will be __________ $\varepsilon$ o. (Dielectric constant of the material = 3.2) (Round off to the Nearest Integer)

Numerical answer type. Work it out, then open the answer.

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Answer: 3

Slab fills half the gap (layer parallel to plates): $C = \frac{\varepsilon_0 A}{d - t + \frac{t}{K}}$ .
$d - t + \frac{t}{K} = 0.5 + \frac{0.5}{3.2} = 0.5 + 0.156 = 0.656$ m.
$C = \frac{2}{0.656}\varepsilon_0 \approx 3.05\varepsilon_0$ .
So the capacitance is $3\varepsilon_0$ (nearest integer).

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