A parallel plate capacitor is made of two square plates of side $a,$ separated by a distance $d\left(d ≪ a\right) .$ The lower triangular portion filled with a dielectric of dielectric constant $K,$ as shown in the figure. Capacitance of this capacitor is:

Question

A parallel plate capacitor is made of two square plates of side

a,

separated by a distance

d\left(d ≪ a\right) .

The lower triangular portion filled with a dielectric of dielectric constant

K,

as shown in the figure. Capacitance of this capacitor is:

A parallel plate capacitor is made of two square plates of side a, separated by a distance d(d ≪ a) . The lower

A parallel plate capacitor is made of two square plates of side a, separated by a distance d(d ≪ a) . The lower

Quantrex Academy · Accepted Answer

Correct answer: B. K ε _ 0 a ^ 2 d(K - 1) ln K

Consider a small element at a distance x. It is a two capacitors in series.

dc = \dfrac{d{c}_{1} \times d{c}_{2}}{d{c}_{1} + d{c}_{2}}

dc = \dfrac{{ε}_{0} . adx}{\dfrac{xtan\theta}{k} + \dfrac{d - xtan\theta}{1}}

∴ dc = \dfrac{{ε}_{0}K . adx}{- xtan \theta\left(K - 1\right) + d . k}

∴ C = {∫}_{0}^{a}\dfrac{{ε}_{0}K . adx}{- xtan \theta\left(K - 1\right) + d . k}

= \dfrac{{ε}_{0}k . a}{tan \theta ( K - 1 )}ln\dfrac{- atan \theta\left(K - 1\right) + d . k}{d . K}

= \dfrac{{ε}_{0}K{a}^{2}}{d\left(K - 1\right)}lnK

A parallel plate capacitor is made of two square plates of side a,...

Options

Correct answer

Step-by-step solution

More from Capacitance