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Resistance Calculation

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Resistance Calculation


1. The resistance $R$ of a wire is calculated using the formula $R=\rho \frac{L}{A}$ where $\rho$ is resistivity, $L$ is length, and $A$ is cross-sectional area. 2. For Question 1, given copper with $\rho=1.7 \times 10^{-8}$ Ohm m, length $L=800$ m, and radius $r=3$ mm $=0.003$ m. 3. Calculate cross-sectional area $A=\pi r^2=\pi (0.003)^2=2.827 \times 10^{-5}$ m$^2$. 4. Compute resistance $R=1.7 \times 10^{-8} \times \frac{800}{2.827 \times 10^{-5}}=0.48$ Ohms. 5. For Question 2, aluminum wire with $\rho=2.82 \times 10^{-8}$ Ohm m, length $L=1500$ m, radius $r=5$ mm $=0.005$ m. 6. Area $A=\pi (0.005)^2=7.854 \times 10^{-5}$ m$^2$. 7. Resistance $R=2.82 \times 10^{-8} \times \frac{1500}{7.854 \times 10^{-5}}=0.54$ Ohms. 8. Question 3: gold wire with $\rho=2.44 \times 10^{-8}$ Ohm m, length $L=500$ m, radius $r=0.006$ m. 9. Area $A=\pi (0.006)^2=1.131 \times 10^{-4}$ m$^2$. 10. Resistance $R=2.44 \times 10^{-8} \times \frac{500}{1.131 \times 10^{-4}}=0.11$ Ohms. 11. Question 4: copper wire length $L=600$ m, circumference $C=0.018$ m, $\rho=1.7 \times 10^{-8}$ Ohm m. 12. Radius $r=\frac{C}{2\pi}=\frac{0.018}{2\pi}=0.002865$ m. 13. Area $A=\pi r^2=\pi (0.002865)^2=2.577 \times 10^{-5}$ m$^2$. 14. Resistance $R=1.7 \times 10^{-8} \times \frac{600}{2.577 \times 10^{-5}}=0.40$ Ohms. 15. Question 5: aluminum cable, $L=1000$ m, circumference $C=0.015$ m, $\rho=2.82 \times 10^{-8}$ Ohm m. 16. Radius $r=\frac{0.015}{2\pi}=0.002387$ m. 17. Area $A=\pi (0.002387)^2=1.789 \times 10^{-5}$ m$^2$. 18. Resistance $R=2.82 \times 10^{-8} \times \frac{1000}{1.789 \times 10^{-5}}=1.58$ Ohms. 19. Question 6: iron wire, $L=2000$ m, $C=0.02$ m, $\rho=1.0 \times 10^{-7}$ Ohm m. 20. Radius $r=\frac{0.02}{2\pi}=0.003183$ m. 21. Area $A=\pi (0.003183)^2=3.182 \times 10^{-5}$ m$^2$. 22. Resistance $R=1.0 \times 10^{-7} \times \frac{2000}{3.182 \times 10^{-5}}=6.28$ Ohms. **Final answers:** Q1: $0.48$ Ohms Q2: $0.54$ Ohms Q3: $0.11$ Ohms Q4: $0.40$ Ohms Q5: $1.58$ Ohms Q6: $6.28$ Ohms