Answer to Question #172105 in Physics for Marie

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:

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