Question

The heater wire in a small stoVe is made of iron ribbon wire 0.1 cm by 0.5 cm in rectangular cross-section and 2 m long. calculate its resistance

Answer 1

The heater wire in a small stove is made of iron ribbon wire 0.1 cm by 0.5 cm in rectangular cross-section and 2 m long. Calculate its resistance.

**Solution.**

The resistance is determined by the following formula:

$$R = \frac {\rho I}{S},$$

where $\rho = 9.71 \cdot 10^{6} \mathrm{ohm} \cdot \mathrm{m}$ is the resistivity of iron, $I = 2 \mathrm{~m}$ is the length of the wire, $S$ is the cross-section area. Find $S$ knowing that the cross-section is rectangular:

$$S = 0.1 \cdot 0.5 = 0.05 \mathrm{cm}^2 = 5 \cdot 10^{-6} \mathrm{m}^2.$$

So we can find the resistance as follows:

$$R = \frac {9.71 \cdot 10^{-8} \cdot 2}{5 \cdot 10^{-6}} = 0.039 \mathrm{ohm}.$$

Answer: 0.039 ohm.