A wire of resistance \(3 \Omega\) is stretched to twice its original length. The resistance of the new wire will be

Given, resistance, \(R_{1}=3 \Omega\)
If \(l\) is the original length of the wire, then after stretching the length of wire is
\(l^{\prime}=2 l\)
From the relation, resistance of a wire,
\(R=\rho \frac{l}{A}\)
where, \(\rho\) is the resistivity and \(A\) is cross-sectional arca.
\(R \propto \frac{l}{A} \)
\( \Rightarrow R \propto \frac{l^{2}}{V} \left[\because A=\frac{\text { Volume }}{\text { Length }}\right]\)
\(\Rightarrow \frac{R_{1}}{R_{2}}=\frac{l_{1}^{2}}{V} \times \frac{V}{l_{2}^{2}} \)
\(\text {Here, } l_{1}=l, l_{2}=2 l \)
\(\Rightarrow \frac{3}{R_{2}}=\frac{l^{2}}{4 l^{2}} \)
\(\text {or } R_{2}=3 \times 4=12 \Omega\)