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The resistivity of a material is a fundamental property that tells us how much the material opposes the flow of electric current. Higher resistivity means the material is less capable of conducting electricity. Resistivity is denoted by the symbol \( \rho \) and is measured in ohm-meters (\( \Omega \cdot m \)). It depends on factors like:

• The type of material, whether it is a conductor or insulator.
• Temperature, as it can affect the flow of electrons.

For copper, which is a great conductor, the resistivity is relatively low compared to other materials, making it ideal for electrical wiring. In our exercise, the resistivity of copper is given as \( 1.72 \times 10^{-8} \Omega \cdot m \). Understanding resistivity helps in designing efficient electrical systems and selecting the right materials for conducting electricity in various applications.

In determining the resistance of a wire, calculating the cross-sectional area is crucial. The cross-sectional area impacts how easily current can flow through the wire. A larger area means less resistance, allowing more current to flow. For circular wires, the cross-sectional area \( A \) can be calculated using the formula for the area of a circle: \[ A = \pi \left( \frac{d}{2} \right)^2 \] where \( d \) is the diameter of the wire. In our specific problem, the diameter was converted from millimeters to meters as \( d = 1.3 \times 10^{-3} \) m. Applying the formula:

• The radius \( r \) becomes \( \frac{1.3 \times 10^{-3}}{2} \) m.
• Therefore, \( A \approx 1.325 \times 10^{-6} \text{ m}^2 \).

This calculation ensures we can accurately determine the wire's resistance, considering its physical dimensions.

Resistance is a measure of how much an object opposes the passage of electric current. In physics, the resistance \( R \) of a wire is derived from the resistivity formula: \[ R = \frac{\rho \cdot L}{A} \] Here, \( \rho \) is the resistivity of the material, \( L \) is the length of the wire, and \( A \) is the cross-sectional area. In the example provided, the given values are:

• \( \rho = 1.72 \times 10^{-8} \Omega \cdot m \)
• \( L = 10.9 \) m
• \( A \approx 1.325 \times 10^{-6} \text{ m}^2 \)

Plugging these values into the formula gives:\[ R = \frac{(1.72 \times 10^{-8} \Omega \cdot m) \cdot (10.9 \text{ m})}{1.325 \times 10^{-6} \text{ m}^2} \]This calculating results in a resistance \( R \approx 1.414 \times 10^{-3} \Omega \), indicating the extent to which the wire resists the flow of electric current. Understanding this formula is essential for predicting how different factors affect resistance and for practical applications in circuit design.