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 (20degreC) resistivity of 130 times 10-8 ohmm. Its temperature coefficient is 3.95times 10 -4 per degreeC. Find the resistivity of the alloy at an operating temperature of 530degreeC. What is in ohm the resistance needed (at operating temperature) if we want the heater to operate with a power output of 1.0 kw when connected to 120 C AC power line? What length of wire is needed if the cross sectional area of the wire is 5.0mm2?

Explanation / Answer

Given that

po = 130 x 10-8 ohm-m

To = 20oC

T = 530 oC

power = 1.0 kW

V = 120 V

A = 5.0 mm2

a)   The resitivity at any temperature is

p = po [ 1 + @ ( T - To) ]

= 138 x 10-8 [ 1 + 3.95 x 10-4 (530 - 20) ]

= 165.80 x 10-8 ohm-m

b)

Resistance = V2 / Power

= 120 * 120 / 1000

= 14.4 ohms

c) We know that

R = p L / A

==> L = R A / p

= 14.4 * 5.0 x10-6 / 165.80 x 10-8

= 43.42 m

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