Q.

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=dN . The dielectric constant of the mth layer is  Km=K1+mN. For a very large N>103 , the capacitance C is αK∈0Adln2 . The value of  α will be___[∈0  is the permittivity of free space]

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Detailed Solution

xm=dNdC=K∈0Adx=K1+mN∈0Adx⇒dC=K1+NxdN∈0Adx⇒1Ceq=∫x=0d dxK∈0A1+xd=1K∈0Aln⁡1+xd0d1d⇒1Ceq=dK∈0Aln⁡(2)⇒Ceq=K∈0Adln⁡2 So, α=1
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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=dN . The dielectric constant of the mth layer is  Km=K1+mN. For a very large N>103 , the capacitance C is αK∈0Adln2 . The value of  α will be___[∈0  is the permittivity of free space]