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Would a 100k ohm resistor produce more heat than a motor that had the same resistance?

+|---------(100k ohms)---------|-

+|---------(100k motor)--------|-

Both circuits have the same amount of current running. Which produces more heat?

Note

One of these circuits is converting electrical energy to mechanical energy as well as heat.

The exact same amout of current is running in either circuit.

The motor is designed to maximize mechanical output.

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  • \$\begingroup\$ This sounds like homework. If so, explain what you're done so far and where you're stuck. \$\endgroup\$ Dec 13, 2012 at 7:32
  • \$\begingroup\$ You might have got a better answer in the Physics Q&A site \$\endgroup\$ Dec 13, 2012 at 10:35
  • \$\begingroup\$ The term "resistance", by itself, is generally only meaningful with motors that are stationary. When motors are turning, their behavior is affected by other parameters in addition to their "DC resistance" (the term for the resistance that would be measured when the motor is not turning). Your 100K resistance figure seems too high to be a plausible DC resistance figure for a motor; what do you mean by the term? \$\endgroup\$
    – supercat
    Dec 13, 2012 at 16:19
  • \$\begingroup\$ Can you just ignore the inductance of the motor? A motor is not a resistance. \$\endgroup\$ Dec 13, 2012 at 16:55

6 Answers 6

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100k is a very high resistance for a motor ..

The resistor will get hotter, because as you say the motor is transferring energy somewhere else. If you put the motor plus whatever it's driving in a sealed calorimeter, and don't have it driving an energy store (winding up a spring, lifting a weight etc), then the total heat rise in the calorimeter will equal the energy put into the system.

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    \$\begingroup\$ Cool. So if you want to cool a circuit off, replace the resistors with motors with loads. Thanks! \$\endgroup\$
    – Vial
    Dec 13, 2012 at 14:19
  • \$\begingroup\$ If you have the motor driving a cooling fan, yes :) But note that a motor is an inductive load not a resistive load, and will usually have a DC resistance less than 10 ohms. \$\endgroup\$
    – pjc50
    Dec 13, 2012 at 14:30
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    \$\begingroup\$ Perhaps a better example is to compare an 8 ohm resistor with an 8 ohm loudspeaker with a 100 watt AC signal going through them. The resistor gets hot silently, the speaker is very loud. Put the speaker in a small perfectly soundproof box, and the box gets hot instead. \$\endgroup\$
    – pjc50
    Dec 13, 2012 at 14:35
  • \$\begingroup\$ Vicky: Although funny, your statement is correct. +1 \$\endgroup\$
    – Al Kepp
    Dec 13, 2012 at 14:41
  • \$\begingroup\$ A motor that is at its full speed only requires enough input to balance its losses so that it stays at that speed. The energy requirement will determine its impedance. A motor can exhibit impedance by virtue of its counter-EMF. You can't just look at the DC resistance of the wiring. \$\endgroup\$
    – Kaz
    Dec 13, 2012 at 21:13
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In theory, the resistor would produce more heat, given identical power supplied and consumed. The motor converts some of the energy to rotational motion. Excess energy is lost in heat (sub-100% efficiency). However, given a resistor with sufficient power-handling capacity, it might simply stay cooler than the motor.

Final answer: it depends. :)

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  • \$\begingroup\$ However, the question asked about heat produced, not temperature. A 100 kΩ resistor conducting 10 mA (for example) dissipates 10 W (Power=I²R) which is 10 J/s of heat. A motor with the same resistance, drawing the same current can be using some of that energy to winch a load raising it's height against gravitational force and thus converting some electrical energy to potential energy and less into heat. \$\endgroup\$ Dec 13, 2012 at 10:33
  • \$\begingroup\$ Note: the predicted quantity of heat is not the same as the predicted temperature - the temperature depends on how good the device is at losing heat to the environment. \$\endgroup\$
    – pjc50
    Dec 13, 2012 at 14:32
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The motor produces more heat. Both will have the same I^2R losses but the motor will have core losses, friction and windage losses and some other losses.

Edit: Let me explain a little more. I'm going to change the example to 10 ohms resistance for the resistor and the motor. Let's also say each is drawing 10 A current. I^2R losses in each is 10^2*10 = 1000 W. The resistor will require a voltage V=I*R = 10*10 = 100 V to produce that current. A motor will require more voltage to produce that current because in addition to the core losses and friction and windage losses, it probably also has a load connected to it which will require more input power. If we say the motor is outputting 10 kW of useful power to the shaft and is 90% efficient, then the total input power required will be 10 kW/.90 = 11.11 kW. Given our 10 A assumption, this would mean the voltage required would be 11.11 kW / 10 A = 1111 V.

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  • \$\begingroup\$ IMO this answer is false. \$\endgroup\$
    – Al Kepp
    Dec 13, 2012 at 14:31
  • \$\begingroup\$ Do you have any reason to say that? \$\endgroup\$
    – Eric
    Dec 13, 2012 at 14:32
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    \$\begingroup\$ I think the confusion is in the different interpretations of the resistance of 100 kΩ. That could refer to resistive losses - a reasonable way of looking at the quantity I²R when analysing the complexities of a motor, but when analysing the circuitry the motor is part of, 100 kΩ probably is the resistance of the component as a whole. In the latter case, I²R is not the power lost due to restitivity, but rather the total power supplied to the motor, which 'I²R losses' only partly account for. \$\endgroup\$ Dec 13, 2012 at 18:27
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    \$\begingroup\$ I don't think that's it. The difference is that the original question asked what would happen if the current and resistance were the same. That's the question I answered. Al Kepp (and others) answered the question "What if the input power and resistance were the same?" \$\endgroup\$
    – Eric
    Dec 13, 2012 at 18:54
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    \$\begingroup\$ +1 for analysis -- as many have noted, depends on the definition of "resistance" in the context of a spinning motor, but I think practically everyone who has responded or commented is correct within the limits of their assumptions. Classic statistical proof of a poorly worded question ;-) \$\endgroup\$ Dec 13, 2012 at 23:01
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It would really depend on the nature of the motor and the resistor. If you had a resistor design thats meant to generate heat, it would - for example nichrome wire or a incandesent light bulb used as a resistor. It would also depend on the rating of the resistor.

Likewise for the motor - it would depend on the design, and what you intend to use this heat for - without knowing your end goal, this is a unanswerable theoratical exercise.

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  • \$\begingroup\$ More like, what are you trying to do? Are we trying to maximise heat generation? Get heat to do work? Making a better clothes drier? \$\endgroup\$ Dec 13, 2012 at 6:58
  • \$\begingroup\$ I am simply doing a thought experiment and trying to calculate where the energy goes in either case. \$\endgroup\$
    – Vial
    Dec 13, 2012 at 7:02
  • \$\begingroup\$ I was thinking that the motor circuit lets off less heat than the resistor due to energy conservation laws. \$\endgroup\$
    – Vial
    Dec 13, 2012 at 7:07
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    \$\begingroup\$ You're right that energy conservation applies and the motor will heat itself up less than the equivalent resistor if it has transferred energy to a load. \$\endgroup\$
    – pjc50
    Dec 13, 2012 at 10:09
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    \$\begingroup\$ @JourneymanGeek: Just curious, how would you design a resistor to not generate heat??? \$\endgroup\$
    – Dave Tweed
    Dec 13, 2012 at 12:26
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The law of conservation of energy

Look here: http://en.wikipedia.org/wiki/Conservation_of_energy

If two devices are connected in parallel in a DC circuit, and they have the same resistance (and current), they consume the same amount of power. (energy = power x time)

Motor then converts part of its energy to motion, the rest of energy is converted to audible noise and heat. But what can a resistor do? It just heats. So a resistor produces more heat.

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The answer depends on what the motor is doing.

If the motor is simply spinning idly at constant speed, then it's generating only heat due to its internal friction, the noise that it generates, and the direct dissipation of heat in its wiring. (The motor can provide some light, too, if it has brushes that generate sparks. But if we count all radiation as heat, we can lump that together with heat.)

If the motor is working against a load, it may be storing energy. For instance, suppose the motor turns a winch, winding a cable onto it, such that a weight is lifted against gravity. There is some loss which turns to heat, but considerable energy is being stored by raising the gravitational potential energy of the weight.

An idle motor also stores energy in the form of rotational kinetic energy, during the period of time when it accelerates. Once it is at full speed, it then consumes power only to balance the losses of energy, so that it maintains speed.

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