A wire of resistance 2 ohms per meter is bent to form a circle of radi

1.	A wire of resistance 2 ohms per meter is bent to form a circle of radius 1 m. The equivalent resistance between its two diametrically opposite points, A and B as shown in the figure is-(a) π Ω (b) π/2 Ω (c) 2π Ω (d) π/4 Ω
Answer» Correct answer is (b) π The resistance of 1m wire is \(2\Omega\) The circumference of the circle is \(2\pi r\) Radius r= 1m So, The total length is \(2\pi\) Resistance of the wire is \(4\pi\Omega\) So, Resistance of each segment is \(2\pi\Omega\) R_eff = \(\frac{2\pi \times 2\pi}{2\pi + 2\pi}\)= \(\frac{4\pi^2}{4\pi}=\pi\)

A wire of resistance 2 ohms per meter is bent to form a circle of radius 1 m. The equivalent resistance between its two diametrically opposite points, A and B as shown in the figure is-(a) π Ω (b) π/2 Ω (c) 2π Ω (d) π/4 Ω

Answer»

Correct answer is (b) π

The resistance of 1m wire is \(2\Omega\)

The circumference of the circle is \(2\pi r\)

Radius r= 1m

So, The total length is \(2\pi\)

Resistance of the wire is \(4\pi\Omega\)

So, Resistance of each segment is \(2\pi\Omega\)

R_eff = \(\frac{2\pi \times 2\pi}{2\pi + 2\pi}\)= \(\frac{4\pi^2}{4\pi}=\pi\)