Question

A $4$ resistance wire is best in the form of a circle find the effective resistance between the ends of a diameter.

Answer 1

The resistance of the resistor is $4\Omega$

When it is bent in a circular form and two point A and B is selected connecting the end point of diameter of the circle, then it will take a parallel combination form where both resistance is of $\frac{R}{2}\Omega$

Therefore effective resistance between point A ad B is $\frac{(\frac{R}{2}\times \frac{R}{2})}{(\frac{R}{2}+\frac{R}{2})}=\frac{\left(\frac{R^2}{4}\right)}{R}$

$=\frac{R}{4}$