An alloy used in a heating element of household heater has a room temperature (2

Question

An alloy used in a heating element of household heater has a room temperature (20 Degree C) resistivity of 1 30x 10-8 0m. Its temperature coefficient is 4.05 x 10^-4 per Degree C. Find the resistivity of the alloy at an operating temperature of 500 Degree C. b) What is in O the resistance needed (at operating temperature) if we want the heater to operate with a power output of 1.5 kW when connected to 120 VAC power line? c) What length of wire is needed it the cross sectional area of the wire is 6.0 mm^2?

Explanation / Answer

As

rho = rho0 (1 + alpha (Tf - Ti))

Then, as Tf = 500 C, Ti = 20 C,

rho = 1.553*10^-6 ohm m   [ANSWER]

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As

P = V^2 / R

Then

R = V^2 / P = 9.6 ohm   [ANSWER]

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As

R = rho L / A

Then

L = R A / rho

As rho = 1.553E-6 ohm m, A = 6.0E-6 m^2, R = 9.6 ohm, then

L = 37.1 m   [ANSWER]

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