A wire of length $L$ and resistance $R$ is stretched uniformly to a length $2L$. The new resistance of the wire is

Solution

1. The resistance of a wire is given by $R=\rho L/A$.
2. Since the volume $V=LA$ remains constant, $A=V/L$.
3. Substituting $A$, we get $R=\rho L^2/V$, implying $R\propto L^2$.
4. When length becomes $2L$, the new resistance $$\begin{array}{rl}{R}^{\prime }& =R(2L/L{)}^2\\ & =4R\end{array}$$.
5. Hence the answer is (B).