A uniform resistance wire is bent into a circle. A total current of 3 A enters the circle at one point and leaves at another point, dividing into two paths along the arcs of the circle. If the current flowing through the shorter arc is 2.4 A , the angle subtended by the shorter arc at the centre of the circle is ______ ^ .

Step-by-step solution

Let the total current be I = 3 A . The current in the shorter arc is I₁ = 2.4 A . By Kirchhoff's Current Law, the current in the longer arc is: I₂ = I - I₁ = 3 - 2.4 = 0.6 A The two arcs of the circle are connected in parallel between the entry and exit points, so the potential difference across them is equal. I₁ R₁ = I₂ R₂ 2.4 R₁ = 0.6 R₂ R₂ R₁ = 2.4 0.6 = 4 For a uniform wire, the resistance of an arc is directly proportional to its length, and therefore directly proportional to the angle it subtends at the centr