When a wire of uniform cross-section `a`, length `I` and resistance `R` is bent into a complete circle, resistance between two of diametrically opposite points will be

Options

A. `R/4`
B. `R/8`
C. 4R
D. `R/2`

Answer

A

Explanation

When wire is bent to form a complete circle then
`2pir=R rArr r=R/(2pi)`
Resistance of each semicircle =`pir=(piR)/(2pi)=R/2`
Thus, net resistance in parallel combination of two semicircular resistance
`R'=(R/2xxR/2)/(R/2+R/2) =((R^(2))/4)/R=R/4`