Answer to Question #108176 in Electric Circuits for Mukelo Madolo

Question

A 500-W heating coil designed to operate from 110 V is made of Nichrone wire 0.0500 mm in diameter a) assuming the resistivity of the Nichrone remains constant at its 20.0 degrees celcius , find the length of wire used. b) What if? Now consider the variation of resistivity with temperature . what power is delivered to the coil of part a) when is is warmed to 1200 degrees celcius?

Answer 1

a)

$$R=\frac{U^2}{P}=\rho\frac{l}{A}=\rho\frac{4l}{\pi d^2}$$

$$\frac{110^2}{500}=\frac{4(100\cdot10^{-8})}{\pi (5\cdot10^{-5})^2}l$$

$$l=0.0475\ m$$

b)

$$P'=\frac{P}{1+\alpha(T-T_0)}$$

$$P'=\frac{500}{1+0.0004(1200-20)}=340\ W$$