Question

Suppose that you want to install a heating coil that will convert electric energy to heat at a rate of 149 W for a current of 0.77 A.

Determine the resistance of the coil. Answer in units of Ω. answer is 251.307

The resistivity of the coil wire is 7.1×10−7 Ω·m, and its diameter is 0.218 mm Find its length. Answer in units of m

Answer 1

We have power P = I^2R therefore Resistance R = P/I^2 = 149/(0.77)^2 i.e R = 251.307 ohm Resistance R = rho l/A = rho l/pi r^2 (where area A = pi r^2) length of wire l = R(pi r^2)/rho where 'r' is radius of wire & rho is the resistivity. Given rho = 7.1 times 10^-7 ohm m r = diameter/2 = 0.218/2 mm = 0.109 mm r = 0.109 times 10^-3 m therefore length l = (251.307) times 3.14 times (0.109 times 10^-3)^2/7.1 times 10^-7 = 1.32 times 10^1 l = 13.2 meter