A hemispherical network of raidus a is made by using a conducting wire of resistance per unit length r. Find the equivalent resistance across OP.

Explanation

In the given ciruit, A,B,C and D are at the same potential by
symmetry.

`R_(eq) = (R_(1)+R_(2))/(4), R_(1)` or, `R_(2) = (pi a)/(2)`
`:. R_(eq) = (ar)/(4)(1+(pi)/(2)) = (ar)/(8) = (2+pi)`