Question

A $4$ ohm resistance wire is bent throught ${180}^o$ at its mid point and the two halves are twisted together. Then the resistance is

• A. $1\Omega$
• B. $2\Omega$
• C. $5\Omega$
• D. $8\Omega$

Answer 1

The correct option is A $1\Omega$

Initially, $R=\frac{\rho l}{A}$ where $\rho =$ resistivity, $l=$ length and $A=$ cross section of wire.
When the wire is bent into two halves and twisted together, the length becomes $l^{\prime }=l/2$ and cross section becomes $A^{\prime }=2A$
Thus, new resistance, $R^{\prime }=\frac{\rho l^{\prime }}{A^{\prime }}=\frac{\rho \left(l/2\right)}{2A}=R/4=4/4=1\Omega$