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

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Correct answer: A. (R θ(2 π-θ))/(4 π^2)

Resistance per unit length = =(R)/(2 π r) Lengths of sections A P B and A Q B are r θ and r(2 π-θ) Resistances of sections A P B and A Q B are aligned & R_1= r θ=(R)/(2 π r) r θ=(R θ)/(2 π) & and R_2=(R)/(2 π r) r(2 π-θ)=(R(2 π-θ))/(2 π) aligned As R_1 and R_2 are in parallel between A and B , their equivalent resistance is aligned & R_ eq =(R_1 R_2)/(R_1+R_2) & =((R θ)/(2 π) · (R(2 π-θ))/(2 π))/((R θ)/(2 π)+(R(2 π-θ))/(2 π))=((R^2 θ(2 π-θ))/(4 π^2))/((R)/(2 π)[θ+2 π-θ])=(R(2 π-θ) θ)/(4 π^2) & aligned

A and B are two points on a uniform ring of resistance R . The A C...

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