The resistivity \( (\rho) \) of aluminum wire is \( 2.6\times10^{-8}\ \Omega\mathrm{m} \). The resistance of the aluminum wire of length \( 60 \) cm and cross-sectional area \( 3\ \mathrm{mm^{2}} \) will be
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 0.0052\ \Omega \)
The resistance of a uniform wire follows from its resistivity, length and area of cross-section.
\( \displaystyle R = \frac{\rho l}{A} \)
Converting to SI units:
\( l = 60\ \mathrm{cm} = 0.60\ \mathrm{m} \)
\( A = 3\ \mathrm{mm^{2}} = 3\times(10^{-3}\ \mathrm{m})^{2} = 3\times10^{-6}\ \mathrm{m^{2}} \)
\( \displaystyle R = \frac{(2.6\times10^{-8}\ \Omega\,\mathrm{m}) \times (0.60\ \mathrm{m})}{3\times10^{-6}\ \mathrm{m^{2}}} \)
\( R = 5.2\times10^{-3}\ \Omega = 0.0052\ \Omega \)