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A capacitor is made of a flat plate of a...

A capacitor is made of a flat plate of area A and a second plate having a stair -like structure as shown in figure. The width of each stair is `a` and the height is `b` . Find the capacitance of the assembly.

Text Solution

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The arrangement is a parallel combination of ther capacitors. Each capaciror has a plate area `A//3`, and the separations between the plates are `d, 2d`, and respectively.
So
`C_(1) =(epsilon_(0)A//3)/(3d)=(epsilon_(0)A)/(3d)`
`C_(2) =(epsilon_(0)A//3)/(2d)=(epsilon_(0)A)/(6d)`
`C_(3)=(epsilon_(0)A3)/3_(d)=(epsilon_(0)A)/(9d)`
As these three capacitances are in parallel, their equivalent capacitance is given by.
`C=C_(1)+C_(2)+C_(3)=(epsilon_(0)A)/(3d)+(epsilon_(0)A)/(6d)+(epsilon_(0)A)/(9d) =(11epsilon_(0)A)/(18d)`
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