Question

A metal wire of resistance $3\Omega$ is elongated to make a uniform wire of double its previous length. This new wire is now bent, and the ends joined to make a circle. If two points on the circle make an angle ${60}^{\circ }$ at the centre, the equivalent resistance between these two points will be-

• A. $\frac{5}{2}\Omega$
• B. $\frac{5}{3}\Omega$
• C. $\frac{12}{5}\Omega$
• D. $\frac{7}{2}\Omega$

Answer 1

The correct option is B $\frac{5}{3}\Omega$

When length doubled, its resistance becomes,

$\because R=\frac{\rho l}{A}=\frac{\rho l^2}{V}\Rightarrow R\propto l^2$
$\Rightarrow R^{{}^{\prime }}=4\times 3=12\Omega$



$R_{AB}=\frac{2\times 10}{2+10}=\frac{5}{3}\Omega$
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.