a wire of resistance 5omega is bent in the form of a closed circle . what is the effective resistance between the two points at ends of any diameter of the circle?
To find the effective resistance between the two points at the ends of any diameter of the circle, we can use the concept of resistances in parallel and series.
When a wire is bent in the form of a closed circle, one complete circumference of the circle creates a closed loop. In this case, we can consider the wire as a combination of two resistors connected in parallel, each having a resistance equal to half of the original wire.
Given that the resistance of the wire is 5Ω, we can calculate the resistance of each half of the wire as 5Ω/2 = 2.5Ω.
Now, when the wire is bent to form a closed circle, the two halves of the wire are connected in parallel. In a parallel connection, the effective resistance (R) is given by the formula:
1/R = 1/R1 + 1/R2
Substituting the resistance values, we have:
1/R = 1/2.5Ω + 1/2.5Ω
Simplifying the equation:
1/R = 2/2.5Ω
1/R = 0.8
R = 1/0.8
R ≈ 1.25Ω
Therefore, the effective resistance between the two points at the ends of any diameter of the circle is approximately 1.25Ω.