Let’s solve for the resistance of a 2.0 m copper wire with a given resistivity and cross-sectional area.
The formula for calculating the resistance [tex]\( R \)[/tex] of a wire is given by:
[tex]\[ R = \frac{\rho L}{A} \][/tex]
Where:
- [tex]\( \rho \)[/tex] is the resistivity of the material (for copper, [tex]\( \rho = 1.7 \times 10^{-8} \ \Omega \cdot m \)[/tex])
- [tex]\( L \)[/tex] is the length of the wire (2.0 m)
- [tex]\( A \)[/tex] is the cross-sectional area of the wire ([tex]\( 2.08 \times 10^{-6} \ m^2 \)[/tex])
Now, substitute the known values into the formula:
[tex]\[ R = \frac{(1.7 \times 10^{-8} \ \Omega \cdot m) \times 2.0 \ m}{2.08 \times 10^{-6} \ m^2} \][/tex]
First, multiply the resistivity by the length of the wire:
[tex]\[ (1.7 \times 10^{-8}) \times 2.0 = 3.4 \times 10^{-8} \ \Omega \cdot m^2 \][/tex]
Next, divide by the cross-sectional area:
[tex]\[ R = \frac{3.4 \times 10^{-8} \ \Omega \cdot m^2}{2.08 \times 10^{-6} \ m^2} \][/tex]
[tex]\[ R \approx 0.016346153846153847 \ \Omega \][/tex]
Thus, the resistance of the copper wire is approximately [tex]\( 0.0163 \ \Omega \)[/tex].
Matching this to the provided options, the closest answer is:
A. [tex]\( 1.6 \times 10^{-2} \Omega \)[/tex]
