A parallel plate capacitor of capacitance C has spacing d between two plates having area A . The region between the plates is filled with N dielectric layers, parallel to its plates, each with thickness δ = d N . The dielectric constant of the m t h layer is K m = K 1 + m N . For a very large…

Question

A parallel plate capacitor of capacitance

C

has spacing d between two plates having area

A .

The region between the plates is filled with

N

dielectric layers, parallel to its plates, each with thickness

δ = \frac{d}{N} .

The dielectric constant of the

m^{t h}

layer is

K_{m} = K (1 + \frac{m}{N}) .

For a very large

N (> 10^{3}),

the capacitance

C

is

α (\frac{K \in_{0} A}{d l n 2}) .

The value of

α

will be____

[\in_{0}

is the permittivity of free space]

Aicharya · Accepted Answer

Let m t h layer is at a distance ‘ x ’ from left plate. Also, let there be a small strip of thickness 'dx' having small capacitance ′ ′ d 1 C ′ ′ with medium ′ ′ K m ′ ′ in between. ⇒ x m = D N Also, d 1 C = d x K m ε 0 A = d x K m ε 0 A = d x K ε 0 A 1 + m N = d x K ε 0 A 1 + x D ⇒ 1 C e q = ∫ d 1 C = ∫ 0 D D d x K ε 0 A D + x 1 C e q = D K ε 0 A l n 2 C e q = K ε 0 A D l n 2 ⋅ Therefore α = 1 `

A parallel plate capacitor of capacitance C has spacing d between two plates having area A . The region…

Solution