Question

The resistance of a wire is $R$. It is bent at the middle by ${180}^{\circ }$ and both the ends are twisted together to make a shorter wire. The resistance of the new wire is

• A. $2R$
• B. $R/2$
• C. $R/4$
• D. $R/8$

Answer 1

The correct option is C $R/4$

Resistance of wire $\left(R\right)=\rho \frac{1}{4}$
If wire is bent in the middle then
$l^{\prime }=\frac{1}{2},A^{\prime }=2A$
$\therefore$ New resistance, $R^{\prime }=\rho \frac{l^{\prime }}{A^{\prime }}=\frac{\rho \frac{1}{2}}{2A}=\frac{\rho l}{4A}=\frac{R}{4}$.