A triangle is constructed using the wires `AB, BC` and `CA` of same material and of resistance `alpha, 2alpha` and `3 alpha` respectively. Another wire of resistance `alpha//3` from `A` can make a sliding conact with wire `BC`. Find the maximum resistance of the network between point `A` and the point of sliding wire with `BC`.

Options

A. `(5)/(11) alpha`
B. `(3)/(8) alpha`
C. `(3)/(11) alpha`
D. `(5)/(8) alpha`

Answer

C

Explanation

(c ) `:. (1)/(R_(eq)) = (1)/((alpha + x)) + (3)/(alpha) + (1)/((5 alpha - x))`
`= (alpha (5 alpha - x) + 3(alpha + x) (5 alpha -x) - 2 (alpha = x))/(alpha (alpha + x) (5 alpha = x))`
`(1)/(R_(eq)) = (5 alpha^(2) - alpha x + alpha^(2) + alphax + 15 alpha^(2) - 3 x^(2) + 12 alpha x)/(a (alpha + x) (5 a - x))`
`R_(eq) = (alpha(alpha + x) (5 alpha =x))/(21 alpha^(2) + 12 alpha x - 3 x^(2)) implies (dR_(eq))/(dx) = 0`
`R_(eq) (max) = (3)/(11) alpha`