Question

The heating element of an electric heater is rated 72 W, 12V and is made of nichrome wire of diameter 0.80 mm and resistivity 1.1 x 10^-6 Ω m. What is the resistance of the heating element and what is the length of the nichrome wire?

Answer 1

(a) We can find the resitance as follows:

$$P=\dfrac{V^2}{R},$$ $$R=\dfrac{V^2}{P}=\dfrac{(12\ V)^2}{72\ W}=2\ \Omega.$$

(b) We can find the length of the nichrome wire as follows:

$$R=\dfrac{\rho L}{A},$$ $$L=\dfrac{RA}{\rho},$$ $$L=\dfrac{2\ \Omega\cdot\dfrac{\pi(0.8\cdot10^{-3}\ m)^2}{4}}{1.1\cdot10^{-6}\ \Omega\cdot m}=0.91\ m.$$