A) 1 : 16
B) 1 : 8
C) 1 : 4
D) 1 : 2
Correct Answer: C
Solution :
Here: Thickness of first wire \[{{r}_{1}}=2r\] The thickness of second wire \[{{r}_{2}}=r\] Using the relation for resistance of wire is, \[R=\frac{S\times l}{A}=S\times \frac{l}{\pi {{r}^{2}}}\propto \frac{l}{{{r}^{2}}}\] Hence\[\frac{{{R}_{1}}}{{{R}_{2}}}={{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{2}}=\frac{{{(r)}^{2}}}{{{(2r)}^{2}}}=\frac{1}{4}\]
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