A wire of length 5m and radius 1mm has a resistance of 1 ohm. What length of the wire of the same material at the same temperature and of radius 2mm will also have a resistance of 1 ohm

1.25 m

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2.5 m

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10 m

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20 m

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Solution

The correct option is D 20 m
$R \propto \frac{l}{r^{2}} \Rightarrow \frac{R_{1}}{R_{2}} = \frac{l_{1}}{l_{2}} \times \frac{R_{2}^{2}}{R_{1}^{2}} \Rightarrow \frac{1}{1} = \frac{5}{l_{2}} \times (\frac{2^{2}}{1}) \Rightarrow l_{2} = 20 m$

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A wire of length 5m and radius 1mm has a resistance of 1 ohm. What length of the wire of the same material at the same temperature and of radius 2mm will also have a resistance of 1 ohm

The correct option is D 20 mR∝lr2⇒ R1R2=l1l2×R22R21⇒ 11=5l2× (221)⇒ l2=20m

The correct option is D 20 m
$R \propto \frac{l}{r^{2}} \Rightarrow \frac{R_{1}}{R_{2}} = \frac{l_{1}}{l_{2}} \times \frac{R_{2}^{2}}{R_{1}^{2}} \Rightarrow \frac{1}{1} = \frac{5}{l_{2}} \times (\frac{2^{2}}{1}) \Rightarrow l_{2} = 20 m$