Answer :
The resistance of the wire is 0.0904 ohms, indicating its opposition to the flow of electric current through it. This value is crucial for determining the behavior of the wire in an electrical circuit.
To determine the resistance (R) of the wire, we apply Ohm's law, which states that the resistance of a conductor is directly proportional to its length (L) and inversely proportional to its cross-sectional area (A). The resistivity[tex](\( \rho \))[/tex]of the material also plays a crucial role, representing its intrinsic resistance to the flow of electric current. The formula [tex]\( R = \frac{\rho \cdot L}{A} \)[/tex] encapsulates these relationships, allowing us to calculate the resistance based on the wire's dimensions and material properties.
[tex]\( 2.8 \times 10^{-8} \, \Omega \cdot \text{m} \) (\( \rho = 2.8 \times 10^{-8} \, \Omega \cdot \text{m} \))[/tex]
In this scenario, the wire has a length of 2 meters [tex](\( L = 2 \, \text{m} \))[/tex], a cross-sectional area of [tex]\( 1.55 \times 10^{-6} \, \text{m}^2 \) (\( A = 1.55 \times 10^{-6} \, \text{m}^2 \))[/tex], and a resistivity of [tex]\( 2.8 \times 10^{-8} \, \Omega \cdot \text{m} \) (\( \rho = 2.8 \times 10^{-8} \, \Omega \cdot \text{m} \))[/tex]. Substituting these values into the formula, we first calculate the product of resistivity and length, then divide this result by the cross-sectional area to obtain the resistance.
The obtained resistance value of [tex]\( 0.904 \, \Omega \)[/tex] indicates the opposition offered by the wire to the flow of electric current. Lower resistance values imply better conductivity, meaning that the wire would allow more current to pass through it with less voltage applied. Understanding the resistance of wires is fundamental in various electrical applications, such as designing circuits, calculating power dissipation, and ensuring efficient energy transmission. Thus, by determining the resistance, we gain insights into the electrical behavior and performance of the wire in practical contexts.
