A parallel plate capacitor of capacitance has spacing between two plates having area

PHYSICS · Subjective · AP · Physics C: Electricity and Magnetism · Conductors and Capacitors · Conductors and Capacitors

Problem

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

\delta = \frac{d}{N}

. The dielectric constant of the

m^{\text{th}}

layer is

K_m = K\left(1 + \frac{m}{N}\right)

. For a very large

N (>10^3)

, the capacitance

C

\alpha\left(\frac{K\epsilon_0 A}{d \ln 2}\right)

. The value of

\alpha

will be \_\_\_\_ [

\epsilon_0

is the permittivity of free space]