I2R and Apparent Temperature
One of the more important points to remember in Electrical Thermograpy is the relationship between load (current through the circuit) and heat. What is often not understood, or misunderstood, is the difference between heat and apparent temperature. Many people mistakenly believe that as current increases that the apparent temperature of a thermal anomaly will immediately increase, and that’s almost never the case.
Heat is inherent in electrical systems, due to the relationship between current and resistance, which is denoted with the combination of Ohm’s Law and Watt’s Law. Watt’s Law states that power (in the form of heat) is the product of current and voltage. Ohm’s Law states that voltage is the product of current and resistance. So, when we combine these laws, we find that heat is the product of current times current, times resistance, or as we often denote it I2R. So in a normal circuit, with no abnormalities, heat will be present because of current passing through the conductors and circuit parts. Abnormal heating is generally caused by an increase in electrical resistance, typically at the junction of a conductor and circuit part.
As you can see, this relationship between current and heat isn’t linear. The relationship between current and apparent temperature isn’t either, but it’s less than exponential. The reason for this phenomenon exists because of how we detect the change in heat output of the connection. Illustrated in Figure One (below), the heat energy is produced at the point of the increased resistance. That physical point isn’t visible to our imager, we see the surface only. Some of that heat energy is lost to conduction through the circuit part, and then the surface itself is subjected to convective cooling. Our imager only sees the energy emitted from the surface, which isn’t the entire amount that is being generated by the current passing through the point of increased resistance.
As load increases, so does the heat output from the connection, and the apparent anomaly temperature, but at differing rates. While the I2R relationship holds true, there’s not really any formulae that are applicable to calculating what the surface temperature might be, relative to the amount of current through the connection. It’s also important to understand that as current increases, the effect on heat output isn’t immediate. This is especially important in trending. When momentary fluctuations in current are noted, there’s no corresponding change in the thermal profile of the anomaly that is readily apparent.
The relationships in electrical anomalies are dynamic, but remember to Think Thermally and you’ll be fine!