Number 10 copper wire (radius = 1.5 mm)is commonly used for electrical installations in homes.What is the voltage drop in 20 m of #10 copper wire if it carries a current of 12 A? (The resistivity of copper is 1.7 × 10−⁸ Ω⋅m. ) A)0.58 V B)0.48 V C)2.7 V D)2.4 V E)0.34 V

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The voltage drop $V$ in a conductor can be calculated using Ohm's Law $V = IR$, where $I$ is the current and $R$ is the resistance. The resistance $R$ of a wire is given by $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity of the material, $L$ is the length of the wire, and $A$ is the cross-sectional area of the wire. The cross-sectional area $A$ of a wire with radius $r$ is $A = \pi r^2$.Given:- $r = 1.5 \, \text{mm} = 1.5 \times 10^{-3} \, \text{m}$- $L = 20 \, \text{m}$- $I = 12 \, \text{A}$- $\rho = 1.7 \times 10^{-8} \, \Omega \cdot \text{m}$First, calculate the cross-sectional area $A$:$$A = \pi r^2 = \pi (1.5 \times 10^{-3} \, \text{m})^2 = \pi (2.25 \times 10^{-6} \, \text{m}^2)$$Then, calculate the resistance $R$:$$R = \rho \frac{L}{A} = 1.7 \times 10^{-8} \, \Omega \cdot \text{m} \cdot \frac{20 \, \text{m}}{\pi (2.25 \times 10^{-6} \, \text{m}^2)}$$$$R \approx 0.048 \, \Omega$$Finally, calculate the voltage drop $V$:$$V = IR = 12 \, \text{A} \cdot 0.048 \, \Omega \approx 0.58 \, \text{V}$$Therefore, the voltage drop in 20 m of #10 copper wire carrying a current of 12 A is approximately 0.58 V.

Number 10 Copper Wire (Radius = 1