A wire of length $L$ and resistance $R$ is stretched so that the length is doubled and area of cross-section is halved. How will its
$(a)$ resistance change ?
$(b)$ resistivity change ?
A wire of length $L$ and resistance $R$ is stretched so that the length is doubled and area of cross-section is halved. How will its
$(a)$ resistance change ?
$(b)$ resistivity change ?
$R =\rho \frac{l}{ A }$
Where $R$ is the resistance and $\rho$ is resistivity.
Initial length of the wire $= L$. So its new length $L^{\prime}=2 L$ and area of its cross-section $= A / 2$
$\therefore$ New area, $A^{\prime}=A / 2$
Now $, R =\rho \frac{ L }{ A }$ and $R ^{\prime}=\rho \frac{ L ^{\prime}}{ A ^{\prime}}$
$(a).$ New resistance $R ^{\prime}=\rho \frac{2 L }{ A / 2} \Rightarrow R ^{\prime}=4 \rho \frac{ L }{ A }$
$\Rightarrow R^{\prime}=4 R$
$(b)$ Resistivity of the wire will be the same.
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