Proof of common sense when maths is lacking concept

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Discussion Overview

The discussion revolves around the relationship between power consumption, resistance, and current in electrical appliances, specifically comparing electric fans and heaters. Participants explore concepts related to ohmic resistance, impedance, and the implications of these factors on power usage in both direct current (DC) and alternating current (AC) contexts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants note that an electric fan has lower power consumption compared to a kettle, despite the fan having smaller resistance, leading to questions about the underlying model.
  • There is a correction regarding the formula for power at constant voltage, with some emphasizing that power is calculated using (I^2)*R rather than I*R.
  • Participants discuss the relationship between resistance and power, with some asserting that less power does not necessarily mean less ohmic resistance.
  • One participant suggests that a fan might have less resistance than a heater, prompting further debate about the actual resistance of different appliances.
  • Confusion arises around the distinction between resistance and impedance, particularly in AC circuits, with some clarifying that inductance affects impedance but not resistance measured by a DC ohmmeter.
  • There is a discussion about how the number of windings in a motor affects its current draw and power consumption, with some arguing that a smaller motor may draw more current and thus use more power.
  • Concerns are raised about the implications of power consumption on torque and field strength in motors, indicating that the relationship is not straightforward.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between resistance, power, and current in electrical appliances. There is no consensus on the specific resistance values of fans versus heaters, and the discussion remains unresolved regarding the implications of these factors in practical scenarios.

Contextual Notes

Participants highlight the importance of distinguishing between resistance and impedance, especially in AC circuits, which introduces additional complexity to the discussion. The conversation also touches on the effects of motor design on power consumption, torque, and current draw, indicating that multiple factors influence these relationships.

Who May Find This Useful

This discussion may be of interest to those studying electrical engineering, physics, or anyone curious about the principles of electricity and power consumption in appliances.

  • #61
TB1,

So you're saying I could force it into that form after partial fractions, interesting.
THOUGH it would take ages to even get to (1) if you didn't have a computer to aid in expanding and simplifying the fraction, wouldn't it?
Yep, lots of work without a computer. But you can see that eq(6) is the same equation as eq(1).
Also, I don't quite see where H came from when you introduced it.
After rationalizing the left side, I multiplied the numerator by what it took to make it look like the right side. The multiplier was "H". Of course, I also had to multiply the denominator by the same multiplier to balance the fraction out.

Ratch
 
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  • #62
milesyoung said:
I'm not quite sure what you mean. I can't see how you could argue that the induced voltage from flux cutting the rotor windings could be attributed to self-inductance.

'Equivalent Circuits' don't always make physical sense, I know, but when you start a motor, a lot of energy goes in. The rate of current reduction will be exponential with a time constant. That can be modeled with a CR series circuit across a parallel resistor. It's a simplification but it even works as the supply volts are reduced.
 

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