Current Electricity
A copper wire is stretched to make it $$0.5\%$$ longer. The percentage change in its electrical resistance if its volume remains unchanged is:
A uniform wire of length $$l$$ and radius $$r$$ has a resistance of $$100\Omega$$. It is recast into a wire of radius $$\dfrac{r}{2}$$. The resistance of new 2 wire will be :
Uniform wire length $$l$$
Redius $$r$$
Resistance$$\quad 100Ω$$
If its radius = $$\cfrac { r }{ 2 } \quad$$
$$\Rightarrow \cfrac { { r }_{ 2 } }{ { r }_{ 1 } } = \cfrac { \cfrac { { l }_{ 2 } }{ { A }_{ 2 } } }{ \cfrac { { l }_{ 1 } }{ { A }_{ 1 } } } $$
volume remians constant
$$\Rightarrow l\times \pi { r }^{ 2 }=\quad l\times \pi \cfrac { { r }^{ 2 } }{ 4 } $$
We know, $$[l=4]$$
$$\Rightarrow { r }_{ 2 }={ r }_{ 1 }\left[ \cfrac { \cfrac { 4 }{ \pi { r }^{ 2 }/4 } }{ \cfrac { 1 }{ \pi { r }^{ 2 } } } \right] $$
$$\Rightarrow { r }_{ 2 }=16{ r }_{ 1 }$$
$$\Rightarrow { r }_{ 2 }=1600\pi $$
A copper wire is stretched to make it $$0.5\%$$ longer. The percentage change in its electrical resistance if its volume remains unchanged is:
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