Heat anticipator component of a room thermostatJoules Heating Law
Definition of Resistive Heating, Ohmic Heating

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What is Joules Heating Law.

This article defines Joules Heating Law and explains how and why resistive heating or ohmic heating occurs in electrical circuits, appliances, or lights.

We use an older Honeywell T87 type thermostat heat anticipator device to explain the relationship between electrical resistance and heat generated by a wire when current flows through it.

Our page top photo illustrates key parts of a traditional room thermostat including the temperature sensing device, including the heat anticipator assembly marked with a yellow arrow.

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Jules Heating Law, Resistive Heating, Ohmic Heating Explained

Heat anticipator adjustment tool from Amps CheckJoules Law Describes Joule Heating or ohmic heating or resistive heating.

Definition: Joule Heating is a synonym for resistive heating or ohmic heating: forms of heat generated when an electric current flows through a resistant path thus losing energy that is in turn given off as heat.

Joule heating can also be described at a more microscopic level:

In the flow of electricity electrons move through the electrical path whose conductivity is limited.

As flowing electrons smack into atoms that comprise the molecules of the conductor (for example the atoms of the molecules of a nichrome heater wire), the electron's energy is transferred into the conductor's molecules in the form of heat.

In this article we use the teensy wound nichrome wire heater of a Honeywell T87 room thermostat heat anticipator as our example resistive Joules-heating device.

The mini amps checker shown in our photo is used to test the current flow through a room thermostat in order to set the heat anticipator correctly.

[Click to enlarge any image]

Formula for Joules Law

The movement of electrical current through a wire produces heat. The amount of heat that will be produced when electrical current flows through a conductor is described as

Joules Law: H = I2 x R x T

where H = heat, I = current in Amps, R= resistance in Ohms, T is duration of current flow in seconds.

The T or time factor is necessary when we are dealing with alternating current.

In a DC circuit we can forget T.

More resistance means that more heat is generated

Joules Law says that the amount of heat (H) generated when current flows through a wire is the product of the square of the current I2 times the resistance of the wire R to which we can add a factor for time T

If we increase the resistance we increase the amount of heat generated.

If we increase the time (over which the circuit is active) we also increase the total amount of heat generated.

It's a bit simplistic, but if I've got this right, as the atoms in a wire resist the flow of electrons heat is generated as a result of collisions and thus the production of kinetic energy. [Really?]

Think of two nice examples, light bulb filaments in incandescent bulbs and the wire element in an electrical fuse. Eventually the heat is enough to light the filament or melt the fuse wire, opening the circuit.

This is opposite of what some readers cited. They explained that at higher resistance less current flowed so less heat was generated.

Honeywell room thermostatThey are right too. Why?

How to calculate the heat output of an electrical-resistance wire

The heat output of an electrical-resistance wire is a function of the supply voltage and the heater resistance (Watts = Voltage2 / Resistance).

Lower resistance produces more heat.

(Paraphrasing from a nice article on electrical resistance heating provided by process technology dot com)

Since in our heat anticipator voltage is constant (say 24V), all we can vary is resistance (moving the slider) where watts (which we can call a measure of heat output) will drop when resistance is increased.

I think part of the trouble we got into was confusion of electrical power with heat. These excerpts are from

Let's assume that the voltage is constant, say 12V. ... if the resistance was 1 Ohm, ... the current would be 12A. ... the total power would be 144W.

If the resistance was 12 Ohms, ... the current would be 1A, ... the total power is 12W. ... lower resistance would emit more heat.

to which another reader replied:

P= VI but that is NOT the heat. ... heat is energy, not power.

The heat a resistor produces is the energy loss given by I2 R.

If you assume a fixed voltage and resistance, then

I= V/R so the heat produced is given by

(V/R)2(R) = V2 / R.

Look at the math. Lower resistance will produce more heat because more current flows.

It's fair to be confused. In the same forum a subsequent reader explains why house wiring under normal loads would not overheat.

In the Heating element example you are assuming that the wire is the only resistance in the circuit and therefore all the voltage is felt across it. With house wiring, the wire delivers electricity to a load that has a much greater resistance than the wires. Therefore the vast majority of the voltage is dropped across the load, and very little across the wires.

The lower the resistance of the wires, the smaller the voltage dropped by them, and the less heating they experience for any given load.

Now if you change resistances, the following happens.

If you use a very large resistance for the element, it drops the majority of the voltage, but limits the current and you get little heating in the element.

If you use a very small resistance, most of the voltage is dropped across the internal resistance of the battery, and you get little voltage across the element and you get little heating.

If you plot the heat (wattage usage) of the element vs the resistance of the element, you will find that the maximum [heating] occurs when the Element's resistance equals that of the internal resistance of the source.

From the same source another reader [we corrected the physicist's spelling] points out the relationship between electrical resistance and wire length.

This is key in understanding how the Honeywell thermostat's heat anticipator adjustment works since sliding the adjuster towards the maximum resistance end (1.2A) is using the full length of coiled wire while sliding the little adjuster towards the minimum resistance end (0.1A) uses the shortest length of wire.

Consider two equal diameter wires with the same resistance but of different materials, say copper and nichrome, since the resistivity of copper is something like 50 times less then that of nichrome the copper wire will be much longer then the nichrome.

Now each is the same resistance so each will suffer the same I2R loss, but since the copper wire is ~50 times the length of the nichrome wire it will be able to dissipate 50 times the heat at any given temperature (this is assuming equal emissitivity).

Which wire will be hotter? The shorter nichrome wire of course. So you need to look at more then just the resistance to evaluate the temperature of a conducting wire.

and finally from yet another commentator:

... the greater the resistance the more likely collisions will occur with the charge flow transferring some of the kinetic energy from an electron and generating heat in the process, but far less often because the amount of charge that is flowing is perhaps half of what it was.

When the resistance is decreased, more charges can flow per unit time and therefore transfer more energy into the resistance than before.

It is less likely that collisions will occur with a lower resistance for the same charge flowing through it, but given the greater amount of charges that make it through the lower resistance, the collisions that do occur happen more often because there are so many more of them.

In colliding with the resistive material they transfer some of their kinetic energy into heat within the resistance.

... the reason a lower resistance takes more energy from the source per unit time (power) is because more charge is allowed to flow when the resistance is lowered therefore transferring more energy from the source to the resistive load ... - retrieved 17 June 2015 original source: Physics Forum,

Calculation Example: Why a Wire with Less Resistance Generates More Heat

Really? Why does a wire with less resistance (Ohms), for example a shorter wire, pass more current (Amps) and why does this less-resistant wire generate more heat than the longer, higher resistant wire?


I = V / R 

That formula tells us that the I or current (Amps) through a conductor (wire) between two points on a circuit is inversely proportional to R the resistance between them (ohms).

I = the current, measured in Amps; I = V / R 

V = the difference in potential between the same two points, measured in Volts; V = I x R

R = the resistance in the conductor or circuit between the same two points, measured in Ohms; R = V / I 

Now let's look not just at electrical resistance but at the heat generated when we change the resistance value or R or Ohms.

In this simplified Joules Law: H = I2 x R

notice that the heat output H of the circuit is the square of the current I x the resistance R.

Watch what happens when we lower the resistance in along the heater wire in a heat anticipator:

Case 1: At a fixed voltage V of 24V, at a resistance R of 24 Ohms

I or current will be I = V / R or I = 1 Amp of current flow

The heat output will be heat H = (1)2 x R or (1) x 1 or 1

We don't care about naming the heat units for this example since all I want to do is show how the heat value changes.

Let's drop the resistance from 24 Ohms down to 1 Ohm - maybe by keeping everything else the same but shortening the wire length:

Case 2: At a fixed voltage V, say 24V, at a resistance R of 1 Ohm

I or current will be I = V / R or I = 24 / 1 which gives us 24V Amps of current flow

The heat output will be heat H = (24)2 x R or (576) x 1 or 576 (we don't care about naming the heat units for this example).

Research & References Explaining Joules Heating, Joules Law, Resistive or Ohmic Heating


Continue reading at ELECTRICAL RESISTANCE vs HEAT GENERATED or select a topic from closely-related articles below, or see our complete INDEX to RELATED ARTICLES below.



Or see HEAT ANTICIPATOR OPERATION that explains the principles of Ohms law and Jules Heating Law applied to a tiny electric heater in a room thermostat.

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