Question

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 :

• A. $l=10\, m$
• B. $l=100\, m$
• C. $l=5\, m$
• D. $l=6.8 \, m$

Answer 1

Answer: (A)

$ 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 =$ ( 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$