Metal wire rods, strands and filaments exhibit resistance values that are based on their metallic composition, cross-sectional area and operating temperature at steady state current flow conditions. The resistance of metallic conductors increases at higher temperatures, which allows for a terminal high temperature with power, in watts, with the nickel-chrome wires used in electric stove elements, for example. Knowing the power flow allows a simple calculation of ohms resistance at a given working voltage, or an approximation of temperature based on comparative resistance values if the type of metal forming the wire is known.

- Skill level:
- Challenging

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## Instructions

- 1
Define the resistance application. In this example of an electric stove, a nickel-chrome, or nichrome, wire in a large coiled electric stove element is rated for 2400 watts at full operating power when glowing cherry red, which is about 871 degrees C. The operating voltage of the stove is 230-volts AC, or alternating current. With this information, you can calculate the wire temperature resistance for the element.

- 2
Calculate the steady-state amperage of the stove circuit at full power by dividing watts by volts to obtain amperes, or amps, current. This is the simple electrical power equation watts power = volts * amps. Since the electrical load is fully resistive and nonreactive, or nonmagnetic, the power factor is 1-to-1 and 2400 watts / 230 volts = 10.435 amps.

- 3
Calculate the steady-state resistance of the wire at operating temperature. The applicable formula is R ohms = E volts / I amps. Therefore, R= 230 volts / 10.435 amps = 22.04 ohms.

## Calculating Resistance at Operating Temperature

- 1
Define the resistance change calculation. With the same stove element at a lower control setting, it only draws 1200 watts of power. At this level, a value of only 130 volts is measured flowing to the element because the temperature control on the stove reduces the voltage. With this information, you can calculate the wire temperature resistance at the lower setting, as well as approximate the lower temperature of the element.

- 2
Calculate the electrical current flow in amps by dividing 1200 watts by 130 volts to yield 9.23 amps.

- 3
Calculate the element wire resistance by dividing 130 volts by 9.23 amps to obtain 14.08 ohms resistance.

- 4
Calculate the temperature change resulting in the lower resistance of the element. If the initial condition is 871 degrees C (cherry red) then you can calculate the temperature from the alpha temperature resistance coefficient formula R = R ref * (1 + alpha (T -- T ref)).

Rearranging, T ref = (1 + (alpha * 1600 -- R / R ref)) / alpha.

Since nichrome wire's alpha is:

alpha = 0.00017 / degree C (as shown in a "Colors of Heated Steel" chart) * 1 degree C / 1.8 degrees F alpha = 0.0009444 ohms / degree F change

then substituting values provides:

T ref = (1 + 0.000944 * 1600 -- (22.04 ohms / 14.08 ohms)) / 0.000944 ohms / degree F T ref = (1 + 1.5104 -- 1.565) / 0.000944 T ref = 0.946 / 0.000944 T ref = 539 degrees C

The lower stove setting results in a lower temperature of 539 degrees Celsius, which would be a dull red in normal daylight, and still enough to cause severe burns.