A and B are two points on a uniform ring of resistance R . The A C B= , where C is the centre of the ring. The equivalent resistance between A and B is

Step-by-step solution

Resistance per unit length = = R 2 r Lengths of sections A P B and A Q B are r and r(2 - ) Resistances of sections A P B and A Q B are aligned & R₁= r = R 2 r r = R 2 & and R₂= R 2 r r(2 - )= R(2 - ) 2 aligned As R₁ and R₂ are in parallel between A and B , their equivalent resistance is aligned & R_ eq = R₁ R₂ R₁+R₂ & = R 2 R(2 - ) 2 R 2 + R(2 - ) 2 = R^2 (2 - ) 4 ^2 R 2 [ +2 - ] = R(2 - ) 4 ^2 & aligned