A ring is made of a wire having a resistance `R_(0) = 12 Omega`. Find the point `A` and `B`, as shown in the figure, at which a current carrying conductor should be connected so that the resistance `R` of the subcircuit between these points is equal to `(8)/(3) Omega`

Options

A. `(l_(1))/(l_(2)) = (1)/(2)`
B. `(l_(1))/(l_(2)) = (5)/(8)`
C. `(l_(1))/(l_(2)) = (1)/(3)`
D. `(l_(1))/(l_(2)) = (3)/(8)`

Answer

A

Explanation

(a) `((A)/(rho l_(1)) + (A)/(rho l_(2))) = (3)/(8)`
`(rho (l_(2) + l_(2)))/(A) = 12`
Solving `(l_(1))/(l_(2)) = (1)/(2)`