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N dielectics are introduced in series in...

N dielectics are introduced in series in a capacitor of thickness D. Each dielectric have width d=D/N & dielectric constant of `m^(th)` dielectric is given by `K_(m)=K(1+m//N).` [Ngtgt`10^(3)`, Area of plates =A] . Net capacitance is given by `(Kepsilon_(0)A)/(alphaDl n2)`. find value of `alpha`

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The correct Answer is:
1

x/m=D/N
`d(1/C)=(dx)/(K_(m)epsilon_(0)A)=(dx)/(Kepsilon_(0)A(1+m/N))=(dx)/(Kepsilon_(0)A(1+x/D))`
`1/(C_(eq))=intd(1/C)=int_(0)^(D)(Ddx)/(Kepsilon_(0)A(D+x))`
`1/(C_(eq))=D/(Kepsilon_(0)A)ln2 `
`C_(eq)=(Kepsilon_(0)A)/(Dl n2).` therefore `alpha=1`
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