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Suppose you are to construct a parallel plate capacitor of $1\mu F$ by using paper sheets of thickness $0.05mm$ as dielectric and a number of circular parallel metal foils connected alternately. If the dielectric constant of paper is $4$ and radius of each foil is $10cm$ then find the number of metal foils needed for this purpose.

Solution:

If there are $n$ foils connected alternately then it can be considered as the parallel combination of $n-1$ capacitors. Thus capacitance,
$$C=(n-1)\frac{\epsilon A}{d}$$
Putting $$C=1\mu F=10^{-6}\mu F$$
$$\epsilon=K\epsilon_0=4*8.854*10^{-12}F/m$$
$$A=\pi r^2=\pi(0.1)^2m^2$$
and $$d=0.05*10^{-3}$$ in the formula $$C=(n-1)\frac{\epsilon A}{d}$$  we get $n=46$
Hence $46$ metal foils are required.