A wire of resistor R is bent into a circular ring of radius r. Equivalent resistance between two points X and Y on its circumference, when angle XOY is a, can be given by-

Options

A. `(Ralpha)/(4pi^(2)) (2pi - alpha)`
B. `R/(2pi)(2pi - alpha)`
C. `R(2pi - alpha)`
D. `(4pi)/(R alpha)(2pi - alpha)`

Answer

A

Explanation

Since, `I = rtheta =r alpha`
Length of arc. XWY = `r alpha`
Resistance of arc. XZY = `R/(2pir) xx ar = (Ralpha)/(2pi)`
Resistance of arc XZY `=R/(2pir) xx r(2pir) xx alpha r = (R alpha(2pi-alpha))/(4pi^(2))`