Electronics Engineering (ELEX) Board Practice Exam

What is the cross-sectional area of a copper wire with a length of 40 m and a resistance of 0.25 Ω, given the resistivity of copper is 0.02 x 10¯⁶ Ω-m?

1. 2.0 mm²

2. 3.2 mm²

3. 4.0 mm²

4. 5.5 mm²

The correct answer is: 3.2 mm²

To find the cross-sectional area of a copper wire, we can use the formula for resistance in relation to resistivity: \[ R = \frac{\rho \cdot L}{A} \] where: - \( R \) is the resistance, - \( \rho \) is the resistivity of the material (in ohm-meters), - \( L \) is the length of the wire (in meters), - \( A \) is the cross-sectional area (in square meters). Given the values: - \( R = 0.25 \, \Omega \), - \( L = 40 \, m \), - \( \rho = 0.02 \times 10^{-6} \, \Omega-m \). Rearranging the formula to solve for \( A \), we have: \[ A = \frac{\rho \cdot L}{R} \] Substituting in the known values: \[ A = \frac{0.02 \times 10^{-6} \, \Omega \cdot m \cdot 40 \, m}{0.25 \, \Omega} \] Calculating the above expression: 1. First calculate \( \rho \cd