Resistivity 80483

The heating coil of the cooker has a resistance of 70.5 ohms and is made of a wire with a diameter of 0.30 mm and a length of 9.8 m. Determine the resistivity of the material from which it is made.

Correct answer:

ρ =  5.085E-7 Ωm

Step-by-step explanation:

$$\begin{gathered} R=70.5\Omega \\ d=0.30\text{mm}\to \text{m}=0.30:1000\text{m}=0.0003\text{m} \\ l=9.8\text{m} \\ r=d/2=0.0003/2=\frac{3}{20000}\doteq 0.0002\text{m} \\ S=\pi \cdot r^2=3.1416\cdot 0.0002^2\doteq 7.0686\cdot 10^{-8}{\text{m}}^2 \\ R=\rho \cdot \frac{l}{S} \\ \rho =\frac{R\cdot S}{l}=\frac{70.5\cdot 7.0686\cdot 10^{-8}}{9.8}=5.085\cdot 10^{-7}\Omega \text{m} \end{gathered}$$

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