Answer to Question #102709 in Electric Circuits for Janay Calice

Question

An electrical space heater contains a Nichrome heating element that has a resistance
of 8.00 Ω at 20.0 C. When 120 V are applied across the heating element, the electric
current heats the Nichrome wire to 1000C.
a) Show the complete calculation of the heating element resistance at 1000 C.
b) Show the complete calculation of the heating element current at 1000 C.
c) Show the complete calculation of the heating element operating power at 1000 C.

Answer 1

Solution. a) Resistance values for conductors at any temperature must be determined through yet another formula:

$$R_t=R_0(1+\alpha(T-T_0))$$

where R_t is resistance for temperature T=1000⁰C; T₀ =20⁰C is initial temperature; α=0.00017 C^-1 temperature coefficient of resistance; R₀=8Ω is resistance for temperature T=20⁰C. Therefore get

$$R_t=8(1+0.00017(1000-20))=9.33\Omega$$

b) Using Ohm's law we get

$$I=\frac{U}{R} = \frac {120V}{9.33\Omega}=12.86A$$

c) Using the electric power formula, we obtain

$$P=UI=120\times12.86=1543.2W$$

Answer. a) R_t=9.33Ω; b) I=12.86A; c) 1543.2W