A parallel plate capacitor with plate area 'A' and distance of… | JEE Main 2021 (25 Jul, Shift 1)

Q86JEE Main 2021 · 25 JUL · SHIFT 1Difficult

Dielectrics

A parallel plate capacitor with plate area 'A' and distance of separation 'd' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as: $\varepsilon(x) = \varepsilon_0 + kx$ , for $\left(0 < x \le \frac{d}{2}\right)$

$\varepsilon(x) = \varepsilon_0 + k(d-x)$ , for $\left(\frac{d}{2} \le x \le d\right)$

Show answer and solution

Answer: (b)

Layers in series: $\frac{1}{C} = \int_0^d \frac{dx}{\varepsilon(x) A}$ ; by symmetry, twice the first half.
$\frac{1}{C} = \frac{2}{A}\int_0^{d/2} \frac{dx}{\varepsilon_0 + kx} = \frac{2}{kA}\ln\left(\frac{2\varepsilon_0 + kd}{2\varepsilon_0}\right)$
$C = \frac{kA}{2\ln\left(\frac{2\varepsilon_0 + kd}{2\varepsilon_0}\right)}$ , so the answer is (b).

Report a mistake

More questions on Dielectrics

The capacitance of a parallel plate capacitor with air as medium is 3. With the…MHT CET 2020 (16 Oct, Shift 1)
The capacitance of a parallel plate capacitor with air as medium is 6 μ F. With the…NEET 2020 (Phase 1)
A parallel plate capacitor having cross-sectional area A and separation d has air in…NEET 2020 (Phase 2)
A parallel plate capacitor has plate of length 'l', width ‘w’ and separation of plates is…JEE Main 2020 (5 Sep, Shift 2)
A parallel plate capacitor has plates of area A separated by distance 'd' between them…JEE Main 2020 (7 Jan, Shift 1)
In a parallel plate air capacitor the distance between plates is reduced to one fourth…MHT CET 2019 (2 May, Shift 2)
A parallel plate capacitor having capacitance 12 pF is charged by a battery to a…JEE Main 2019 (10 Jan, Shift 2)
Two identical parallel plate capacitors, of capacitance C each, have plates of area A…JEE Main 2019 (12 Apr, Shift 1)

Dielectrics question from JEE Main 2021 (25 Jul, Shift 1)

More questions on Dielectrics