A wire of resistance `12 Omega m^(-1)` is bent to from a complete circle of radius `10 cm`. The resistance between its two diametrically opposite points, `A` and `B` as shown in the figure, is

Options

A. `0.6 pi Omega`
B. `3 pi Omega`
C. `6 pi Omega`
D. `6 pi Omega`

Answer

A

Explanation

(a) Circumference of circule `= 2 xx pi (10)/(100) = (2 pi)/(10) = (pi)/(5)`
Resistance of wire `= 12 xx (pi)/(5) = (12 pi)/(5)`
Resistance of each section `= (12 pi)/(10) Omega`
`:.` Equivalent resistance
`R_(eq) = ((12 pi)/(10) xx (12pi)/(10))/((12pi)/(10) + (12 pi)/(10)) = (6 pi)/(10) = 0.6 pi Omega`