If a wire of resistance $R$ is melted and recasted to half of its length, then the new resistance of the wire will be
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(a) $R \propto {l^2} \Rightarrow \frac{{{R_1}}}{{{R_2}}} = {\left( {\frac{{{l_1}}}{{{l_2}}}} \right)^2}$$ \Rightarrow \,\frac{R}{{{R_2}}} = {\left( {\frac{l}{{l/2}}} \right)^2} = 4 \Rightarrow {R_2} = \frac{R}{4}$.
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