Physics Asked by Dinis on July 3, 2021
The heat dissipated by a resistor is given by the formula
$$ I^2 R $$
Any circuit portion has an equivalent resistance. Does that mean that the heat dissipated by any circuit portion, doesn’t matter what it is, can be calculated using that formula?
If not, please explain why and how does it correlate to the equivalent resistance.
If yes, then the following doesn’t make sense:
If an electric motor running with 230V AC draws 100 W:
the current is:
$$ I = P/V = 100/230=0.43 A $$
the resistance is:
$$ R = V/I = 230 / 0.43 = 529Ohms $$
Therefore, the heat dissipated by it is the same as its wattage:
$$ H = I^2*R = 0.43^2*529 = 100 W $$
If it dissipates all it consumes as heat, then all the torque it produces would be "free energy", which, obviously, doesn’t make sense.
Clearly I’m missing something here. Because either answer doesn’t make sense to me and one of them must be correct because they are the opposite of each other.
The heat dissipated by a resistor is given by the formula $$I^2R$$
No it's not. $I^2R$ represents the power delivered to a resistance by a DC source. DC refers to current that is constant in direction. If all of the power delivered to the resistor is stored as internal energy and transferred out of the system by heat, then the energy transferred to the surroundings is $$Q = I^2RDelta t$$ where $Delta t$ is the time interval for which the power has been delivered.
$$ H = I^2R = 100W $$
Heat has units of joules, not watts, leading to the conclusion that the formula is incorrect. Moreover, the current delivered is AC, so it's direction varies periodically and this equation cannot be directly applied to obtain the power delivered either. The motor can also not be modelled as a simple resistor, hence the mistakes.
Correct answer by Cross on July 3, 2021
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