In the given circuit 'a' is an arbitrary constant. The value of m for which the equivalent circuit resistance is minimum , will be `(sqrt(x)/(2))`. The value of x is _______.

Answer

3

Explanation

Req `= (ma)/(3) + (a)/(2m)`
Req is function of m
`therefore ` for Minima of m
`(dep_("Req"))/(dm) = 0`
`(a)/(3) + (a)/(2) ((-1))/(m^(-2)) = 0`
`(1)/(3) = (1)/(2m2^(2))`
`m^(2) = (3)/(2)`
`m = sqrt((3)/(2))`