JEE MAIN - Physics (2019 - 9th January Morning Slot - No. 15)
A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume remains unchanged is :
2.0 %
2.5 %
1.0 %
0.5 %
Explanation
We know,
$$R = {{\rho l} \over A}$$
and Volume (V) = A$$l$$
$$ \Rightarrow $$ A $$=$$ $${V \over l}$$
$$ \therefore $$ $$R = {{\rho {l^2}} \over v}$$
$$ \therefore $$ $${{\Delta R} \over R} = 2{{\Delta l} \over l}$$
$$=$$ 2 $$ \times $$ 0.5
$$=$$ 1%
$$R = {{\rho l} \over A}$$
and Volume (V) = A$$l$$
$$ \Rightarrow $$ A $$=$$ $${V \over l}$$
$$ \therefore $$ $$R = {{\rho {l^2}} \over v}$$
$$ \therefore $$ $${{\Delta R} \over R} = 2{{\Delta l} \over l}$$
$$=$$ 2 $$ \times $$ 0.5
$$=$$ 1%
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