Question

A metal has a conductivity at room temperature of 4.64*10^-7 s/m. What is the resistance of a wire 1.6mm in diameter and 45 cm long? If the wire is carrying a current of 1.3 amps, what is the voltage applied to the wire and electric field within the wire?

Answer 1

Dear Student
$$\begin{gathered} R=\frac{L}{\sigma A} \\ R=\frac{45\times {10}^{-2}m}{4.64\times {10}^{-7}\times \mathrm{\pi }\times {\left(0.8\times {10}^{-3}\right)}^2} \\ R=\frac{45\times {10}^{-2}m}{4.64\times {10}^{-7}\times 3.14\times 0.64\times {10}^{-6}}=4.82\times {10}^{11}Ohm \end{gathered}$$
V=IR
V =1.3 x 4.82 x10¹¹ = 6,27x10¹¹ V

E = V/d = 6,27x10¹¹ V/45 x 10^-2 =0.139x10¹³ Nm/C

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