An electric heater has a Nichrome heating element with a resistance of 9 Ω at 20oC. When 112 V are applied, the electric current heats the Nichrome wire to 1090oC. What is the operating wattage of this heater? (The temperature coefficient of resistivity of Nichrome is α = 0.0004 Co-1)

975.28 W.

Explanation:

Using,

R' = R(1+αΔt) Equation 1

Where R' = Resistance at the final temperature, R = Resistance at the initial temperature, α = temperature coefficient of resistivity of Nichorome, Δt = Temperature rise.

Given: R = 9 Ω, α = 0.0004/°C, Δt = 1090-20 = 1070 °C

Substitute into equation 1

R' = 9(1+0.0004×1070)

R' = 9(1.428)

R' = 12.862  Ω.

Note: Operating wattage of the heater means the operating power of the heater

The power of the heater is given as,

P = V²/R' Equation 2

Where P = Operating wattage of the heater, V = Voltage, R' = Operating resistance.

Given: V = 112 V, R' = 12.862 Ω

Substitute into equation 2

P = 112²/12.862

P = 975.28 W.