What is the relationship between electrical resistance and heat generated by a wire, circuit or electrical device?

This article uses 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.

In the related article series we explain how adjusting the heat anticipator pointer changes the heat output of the anticipator that in turn changes the behavior of the room thermostat to turn the burner off sooner or later with respect to the actual room temperature.

Our page top photo illustrates key parts of a traditional room thermostat including the temperature sensing device, thermostat switch, and the heat anticipator assembly.

Why Higher Current (Amps) OR Lower Electrical Resistance Can Generate More Heat

17 June 2015 Adam Williams said: Why Higher Electrical Resistance Means Less Heat is Generated in a Heat Anticipator Circuit

I have an OLD ('70s) honeywell class 2 lr1620 and the anticipator dial has an arrow indicating LONGER in the direction of the HIGHER numbers (like the ones you show above).

It is a completely different dial with a metal connector used to set the Amps using your fingernail.

It would seem that the direction of the "LONGER" arrows in both units is not a mistake by Honeywell, ....

My heating unit is reaching temp, shutting down (mercury switch tipping), then failing to start up again, despite the mercury switch being clearly engaged.

I thought it might be the anticipator which is set on 0.4. Any ideas? Thanks Adam. Melbourne Australia boogweig@gmail.com

These remarks were posted originally

at HEAT ANTICIPATOR OPERATION

About the photo above: The imprint "LONGER" is seen at the low-number end of the Amps scale on this thermostat heat exchanger. However a closer examination of Honeywell T87 Thermostats will show that on nearly all of them properly produced with the word "LONGER" stamped at the low-number end of the scale also sport an arrow pointing towards the higher numbers. [Click to enlarge any image]

Honeywell was saying: for longer heat-on times move the pointer in the direction of the arrow (towards higher Amps numbers). I think they printed Longer where they did because that'w where the scale's design gave room for the text.

Reply: don't confuse resistance (Ohms - Ω ) with current (Amps)

Adam,

The labeling of numbers and arrows on a thermostat heat anticipator circuit can be confusing but the following are true on that circuit:

1. Higher numbersOn the Honeywell thermostat heat anticipator scale and on most other thermostats refer to higher current measured in Amps.
2. Higher current flow through the heat anticipator wire means that more heat will be produced. The heat anticipator is getting a constant 24VAC.
   
   This is in accordance with Joule's first law, or the Joule-Lenz law that tells us that
   
   The amount of heat or power of heating generated by an electrical conductor is proportional to the product of its resistance and the square of the current. P = I² R
   
   Details of this heating effect are at JOULES HEATING LAW
3. Generating more heat at the heat anticipator will turn the heating system off sooner - it is "anticipating" the temperature to which the heating system will raise the room around the thermostat for a brief time after the heater has actually turned off.
4. Generating less heat at the heat anticipator will allow the heating system to stay on longer - it is NOT "anticipating" or "pre-warming" the thermostat to fool it into thinking the set temperature has been reached
5. Higher numbers on the heat anticipator Current scale in Amps means heat stays on longer

Current flowing through a wire that acts as a resistor will convert electrical energy to heat.

If we keep the voltage unchanged and just change the length of a wire, a longer wire produces more resistance to current flow (resistance in Ohms) and a shorter wire produces less resistance to current flow.

Less Electrical Resistance = More current flow = more heat is produced

More Electrical Resistance = Less current flow = less heat is produced

The use of a thin nichrome or chromium wire in a heat anticipator is chosen because at the same total resistance of the electrical circuit, that wire will both reach a higher wire-temperature than would a thick copper wire, and it will also resist burning up when heated.

That's true even though that thin chromium wire is itself considered "high resistance" wire - a fact that can lead us astray.

To get the same total resistance the copper wire would be about 50x longer than the chromium wire and would thus be able to dissipate 50x more heat over its length than would the chromium wire.

Example: the heat given off by a resistor is its energy loss I²R. Keeping Voltage AND Resistance fixed, I = Voltage / Resistance and heat produced is given by (V / R)² (R)= V² / R.

When we lower the resistance R we will see more current and thus more heat.

Really? That's counter-intuitive to the general observation that "if it's easier for electricity to flow through a wire then it loses less energy so gives off less heat.

Here's what an electronics forum discussion explained: two things can be true at once:

Any given resistor can dissipate the same amount of power. It just depends on the product of voltage and current

P = V x I or Power = Volts x Amps

Since V = I x R and I = V / R the expression for the power can be rewritten as

P = V x (V / R) or

P = V² / R

or as

P = (I x R) x I or

P = I² x R

The first equation (P = V x I ) suggests that a higher resistance would be better [to obtain a higher current]

while the second (P = I² x R ) shows that a lower resistance would be better [to obtain a higher voltage or less voltage drop]

So it depends on the application if it is easier to generate a higher current or a higher voltage and you have to choose the resistor accordingly.

Sources & Discussion of Which Heats-up more: high-resistance wire or low-resistance wire circuits

• "Is higher or lower resistance wire able to heat up more?, Electrical Engineering StackExchange, retrieved 2017/10/31, original source: https://electronics.stackexchange.com/ questions/219212/is-higher-or-lower-resistance-wire-able-to-heat-up-more-are-there-other-factors
• "Resistance of a heating element", Physics Forums, retrieved 2017/10/30, original source: https://www.physicsforums.com/threads/resistance-of-a-heating-element.5608/
  
  Paraphrasing, adapting, and commenting on the above: If the electrical resistance in a circuit is very low, electrons can move right through without losing much energy [in the form of heat], whereas if the resistance is high the electrons meet resistance, lose energy, and that lost energy is given off as heat. (P=VI & V= IR).
  
  But we also see that P=VI is not a measure of heat, it's a measure of power.
  
  The heat given off by a resistor is I ² R
  
  When we keep the same voltage (24VAC on a thermostat heat anticipator circuit) if we keep the same resistance (Ohms) then the heat produced is given by (V/R)² (R) = V² R.
  
  Dividing the square of the voltage by the circuit resistance means that as we lower the resistance we see more heat produced.
  
  Why does this make sense for the little heater in the thermostat's heat anticipator? Because for that circuit, the little heater wire is the only thing in the circuit. Nothing else is limiting current flow through that little wire, so it gets warm - or even hot.
  
  Conversely, in a house wire circuit that say powers a light bulb or a toaster, the bulb or toaster is providing a much higher resistance than the circuit wire bringing power to that device. So the device heats up enormously more than the circuit wire itself. (And of course the circuit wire is #14 or #12 coppe wire while the heating up wires in the light bulb (tungsten) or toaster (nichrome wire) are quite thin.
  
  Here are the most-helpful comments of this explanatory discussion:
  
  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 occurs when the Element's resistance equals that of the internal resistance of the source.
  
  This is also the reason for impedance matching in electronic circuits; The maximum signal strength is transfered when the impedance of output and input match.
  
  Sooo,
  
  If you use a very small resistance AND the circuit design is such that the voltage drop is across the resistance of the heating-wire-circuit, [nothing else in the circuit is limiting current flow] you will get more heating. That's what we have in a heat anticipator internal-nichrome-wire-heater device.
  
  The comparatively large #18 copper thermostat wire has maybe 50 times less resistance than the short length of nichrome wire in the thermostat heat anticipator's heater. So the 24VAC fed into the little heater warms up the nichrome wire - where it's functioning similarly to the filament in a light bulb fed by #14 copper wire in a house circuit.
  
  When we adjust the heat anticipator to a higher Amps number we shorten the nichrome wire to lower its resistance still further, more current is pushed through it and it gets still hotter. - Ed.

Does Setting the Thermostat Heat Anticipator to a Higher Number Cause our Heating System to Run Longer?

Let's look at our little heat anticipator mechanism shown above.

On all of Honeywell's heat anticipators, either by the direction of an arrow or by the imprint of the word LONGER we are told that the LOWER Amps (current) numbers on the heat anticipator scale will run the heat longer.

That's because at higher currents (Amps) more heat will be generated while at at lower currents less heat is generated in the wire that comprises the heat anticipator's actual heater.

When the heat anticipator generates more heat (higher Amps) it is pre-warming the thermostat's temperature sensor more so heat shuts off sooner or the heater runs for a shorter time.

As we slide the heat anticipator pointer to the left (towards 1.2A - the highest number on the scale), keeping voltage the same, current will run through a SHORTER length of nichrome wire - the total resistance will be less, more current flows, the wire will get more hot, and heat generated by the heat anticipator will be more.

When the heat anticipator generates less heat (lower Amps) it pre-warms the thermostat's temperature sensor less so heat shuts off later,or the heater runs for a longer time.

As we slide the heat anticipator pointer towards the right (towards 0.10A), current has to run through a longer length of nichrome wire - resistance will be more, the current flow will be less, and the heat generated by the heat anticipator will be less.

When the heat anticipator generates less heat it is warming the thermostat's bimetallic spring less, so the thermostat thinks the room is cooler, so the building heating system will run slightly longer and a bit more heat will be delivered to the building from its heating system.

Basically, electrical resistance (measured in Ohms) is the resistance of a wire to the flow of electrical current. Electrical energy is needed to push current (measured in Amps) through a the resistance of a wire. That electrical energy will be dissipated in the form of heat, heating up the wire in the process.

This heating is called Joule heating (James Prescott Joule) or ohmic heating or resistive heating.

The formula for Joule Heating (P) (JOULES HEATING LAW) tells us that the amount of heat generated by a wire is proportional to the product of its resistance and the square of the current passing through it, or

P = I² R

P = power or energy (converted from electrical energy to heat) or the heat produced by a resistor (or wire)

I = current (amps) through the resistor or wire

R = resistance (Ohms)

Ohm's Law (OHM's LAW) says that the current through a wire is proportional to the voltage, or

I = V / R

I = current through the wire (in Amps)

V = voltage measured across the wire (in Volts)

R = resistance of the wire (in Ohms)

If we keep Voltage unchanged and Resistance unchanged

I = V/R or Current = Volts / Resistance,

and looking at the two formulas we just gave, we can substitute (V/R) for I and the

heat produced is

(V/R)² x R = V² / R

Which tells us that lower resistance (R) will produce higher current. Therefore lower resistance produces more heat.

So why don't low-resistance building electrical wires get really hot? Because most of the voltage drop is across the load (light bulb, toaster, dishwasher) rather than across the wire.

It is the resistance of the load, the appliance, light bulb, or whatever the electrical circuit is powering that limits current flow through the electricl wire in a normal building circuit.

In fact if the appliance has a short circuit or failure so that it begins to pass more current than is safe for the circuit, the circuit breaker is designed to open or trip to stop the flow of electricity.

Details about electrical resistance heating

Other readers commented that previously we had not properly explained the properties of electrical resistance and that longer heat on times would be associated with less heat output from the heat anticipator that would occur at higher rather than lower resistance.

The wire wound resistor used in a heat anticipator converts some electrical power into heat. The electrical resistance of a conductor is responsible for the generation of heat.

Joules Law Describes Joule Heating or ohmic heating or resistive heating

This discussion is now found at JOULES HEATING LAW - live link is given just below.

...

Continue reading  at HEAT ANTICIPATOR OPERATION or select a topic from the closely-related articles below, or see the complete ARTICLE INDEX.

Or see these

Recommended Articles

• DEFINITION OF AMPS, ELECTRICAL CURRENT
• DEFINITION OF OHMS, ELECTRICAL RESISTANCE
• HEAT ANTICIPATOR OPERATION
  • HEAT ANTICIPATOR FUNCTION
  • HEAT ANTICIPATOR REQUIREMENTS
• HEAT ANTICIPATOR EFFECTS on ROOM TEMPERATURE
• ELECTRICAL RESISTANCE vs HEAT GENERATED
• FURNACE CONTROLS & SWITCHES
• HEAT ANTICIPATOR ADJUSTMENT
• HEAT ANTICIPATOR ADJUSTMENT - T87
• HEAT ANTICIPATOR SET & TEST by AMMETER
• HEAT ANTICIPATOR THERMOSTAT SOURCES
• JOULES HEATING LAW - Definitions & an explanation of resistive heating or resistance heating, ohmic heating, & Joules Heating
• TEMPERATURE RESPONSE of ROOM THERMOSTATS

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INDEX to RELATED ARTICLES: ARTICLE INDEX to HVAC THERMOSTATS

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