A uniform metallic wire carries a current $2\,A$. when $3.4\,V$ battery is connected across it. The mass of uniform metallic wire is $8.92 \times 10^{-3} \,kg$. density is $8.92 \times 10^3\,kg / m ^3$ and resistivity is $1.7 \times 10^{-8} \Omega- m$. The length of wire is $l=............\,m$
JEE MAIN 2023, Medium
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$I =2\,A$
$\Delta V =3.4\,V$
Using Ohm's Law
$R =\frac{3.4}{2}=1.7 \Omega$
$1.7=\frac{\rho L }{ A }$
$L =\frac{1.7( A )}{\rho}$
$M =(\text { density volume })$
$Volume =\frac{8.92 \times 10^{-3}}{8.92 \times 10^3}=10^{-6}$
$L ^2=\frac{1.7}{\rho}\left(10^{-6}\right)=\frac{1.7}{1.7} \times 10^2$
$L =10\,m$
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