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.

Explanation

`C_1 = eplision _0 A / 3d , C_2 = eplision _0 A / (d+b) `
` C_3 = eplision_0 A / 3(d + 2b)`
The surface area at each is equal to A / 3 . Then the three capacitor is parallel combination .
` C = C_1 + C_2 + C_3 `
`= eplision_0 A / 3d + eplision_0 A / 3 (d + b ) + eplision_0 A / 3 (d + 2b) `
` = eplision_0 A / 3 (3d^(2) + 6bd + 2b^(2) ) / d ( d+ b ) (d + b) `.