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Question

How does the resistance of a wire change when its radius is tripled its material is changed to one whose resistivity is three times? 


A
Resistance increases 3 times
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B
Resistance decreases 3 times
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C
Resistance will be 9times
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D
Resistance will be 2 times
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Solution

The correct option is D Resistance decreases 3 times
Resistance of the wire      $$R = \rho\dfrac{L}{\pi r^2}$$          $$\implies R\propto \dfrac{\rho}{r^2}$$

Given :   $$\rho' = 3\rho$$       $$r' = 3r$$

$$\therefore$$   $$\dfrac{R'}{R} = \dfrac{\rho'}{\rho}\dfrac{r^2}{(r')^2}  = \dfrac{3}{3^2} = \dfrac{1}{3}$$

Thus resistance of the wire will decrease by 3 times.

Physics

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