A thick wire is stretched so that its length become two times. Assuming that there is no change in its density, then what is the ratio of change in resistance of wire to the initial resistance of wire
Medium
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(c) In stretching $R \propto {l^2}$ $ \Rightarrow $ $\frac{{{R_2}}}{{{R_1}}} = \frac{{{l_2}^2}}{{{l_1}^2}}$ $ \Rightarrow $ $\frac{{{R_2}}}{{{R_1}}} = {\left( {\frac{2}{1}} \right)^2}$
$ \Rightarrow $${R_2} = 4{R_1}$. Change in resistance $ = {R_2} - {R_1} = 3{R_1}$
Now, $\frac{{{\rm{Change}}\,\,{\rm{in}}\,\,{\rm{resistance}}}}{{{\rm{Original}}\,\,{\rm{resistance}}}} = \frac{{3{R_1}}}{{{R_1}}} = \frac{3}{1}$
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