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.

Options

A. `(2Ain_(0))/(2(d+b))`
B. `(Ain_(0)(3d^(2)+6bd +2b^(2)))/(3d(b+d)(d+2b))`
C. `(Ain_(0)(d^(2)+2bd +b^(2)))/(3d(d+b)(d+2b))`
D. `(2A in_(0)(d^(2)+2bd +b^(2)))/(3d(d+b)(d+2b))`

Answer

B

Explanation

In Equivalent circuit `C_(1),C_(2),C_(3)` are parallel
`C_(1)=(A in_(0))/(3d),C_(2)=(A in_(0))/(3(d+b)),C_(3)=(A in_(0))/(3(d +2b))`.