Nikelin and brass

Calculate the length of brass wire (ró=0.08 microohm m) and nickel (ró=0.4 microohm m) with a diameter of 0.5 mm, which has a resistance of 1 ohm

Correct answer:

a =  245.4 m
b =  49.1 m

Step-by-step explanation:

$$\begin{gathered} {\rho }_1=0.08\cdot 10^{-8}\doteq 8\cdot 10^{-10}\Omega \text{m} \\ {\rho }_2=0.4\cdot 10^{-8}\doteq 4\cdot 10^{-9}\Omega \text{m} \\ d=0.5\text{mm}\to \text{m}=0.5:1000\text{m}=0.0005\text{m} \\ R=1\Omega \\ R=\rho \cdot l/S \\ r=d/2=0.0005/2=\frac{1}{4000}\doteq 0.0003\text{m} \\ S=\pi \cdot r^2=3.1416\cdot 0.0003^2\doteq 1.9635\cdot 10^{-7}{\text{m}}^2 \\ a=\frac{R\cdot S}{{\rho }_1}=\frac{1\cdot 1.9635\cdot 10^{-7}}{8\cdot 10^{-10}}=245.4\text{m} \end{gathered}$$

$b=\frac{R\cdot S}{{\rho }_2}=\frac{1\cdot 1.9635\cdot 10^{-7}}{4\cdot 10^{-9}}=49.1\text{m}$

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