In the given circuit 'a' is an arbitrary constant. The value of m for which the equivalent circuit resistance is minimum, will be x 2 . The value of x is _____ .

Step-by-step solution

Left part of the resistors are connected in parallel, hence R 1 = a m 3 . Similarly, for the right part of the resistors we can write, R 2 = a 2 m . Therefore, equivalent resistance will be, R = a m 3 + a 2 m Differentiating both sides w.r.t m to observe critical points, we get d R d m = a 3 + a - 1 2 m 2 = 0 ⇒ a 3 = a 2 m 2 ⇒ m = 3 2 Thus, x = 3 .