A parallel plate capacitor of capacitance \( C \) has spacing \( d ...

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A parallel plate capacitor of capacitance \( C \) has spacing \( d \) between two plates having area \( \mathrm{A} \). The region between
P the plates is filled with \( \mathrm{N} \) dielectric layers, parallel to its

W plates, each with thickness \( \delta=\frac{\mathrm{d}}{\mathrm{N}} \). The dielectric constant of the \( \mathrm{m}^{\text {th }} \) layer is \( \mathrm{K}_{\mathrm{m}}=\mathrm{K}\left(1+\frac{\mathrm{m}}{\mathrm{N}}\right) \). For a very large \( \mathrm{N} \) \( \left(10^{3}\right) \), the capacitance \( \mathrm{C} \) is \( \alpha\left(\frac{\mathrm{K} \in_{0} \mathrm{~A}}{\mathrm{~d} / \mathrm{n} 2}\right) \). The value of \( \alpha \) will be . [ \( \in_{0} \) is the permittivity of free space]
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