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  4. A wire of radius r has resistance R. If it is stretched to a radius of (3r/4) . Its resistance becomes

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Q. A wire of radius r has resistance R. If it is stretched to a radius of $ \frac{3r}{4} $ . Its resistance becomes

MGIMS WardhaMGIMS Wardha 2013

Solution:

The resistance of a wire of length $ l, $ area of cross-section A and specific resistance p is. $ R=\rho \frac{l}{A} $ Also $ volume=length\times area $ $ =lA=constant $ $ {{l}_{1}}{{A}_{1}}={{l}_{2}}{{A}_{2}} $ $ \frac{{{l}_{1}}}{{{l}_{2}}}=\frac{{{A}_{2}}}{{{A}_{1}}}=\frac{\pi \left( \frac{3r}{4} \right)}{\pi {{r}^{2}}}=\frac{9}{16} $ $ \frac{{{R}_{1}}}{{{R}_{2}}}=\frac{{{l}_{1}}}{{{l}_{2}}}\times \frac{{{A}_{2}}}{{{A}_{1}}} $ $ =\frac{9}{16}\times \frac{9}{16}=\frac{81}{256} $ $ {{R}_{2}}=\frac{256{{R}_{1}}}{81}=\frac{256R}{81} $