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Electrical Power Equation Contradiction

  1. Aug 19, 2013 #1
    We know that the rate at which electrical work is done (electrical power) is defined as:

    P = I2*R

    , or:

    P = V2/R

    The formula P = V2/R implies that if the resistance of an electrical component (R) (for example, a light bulb) is decreased, the power consumption (P) will increase hence the light bulb will grow brighter. But the formula P = I2*R implies that if R is decreased, P is also decreased and the light bulb will get dimmer.

    They can't both be right. What is your answer to this apparent anomaly?

    Thank you.
    Last edited: Aug 19, 2013
  2. jcsd
  3. Aug 19, 2013 #2


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    Gold Member

    No, that would imply that we could decrease the resistance without changing the current which doesn't make sense. "I" will increase as the resistance decreases and since the "I" term is squared while the "R" term is not squared, clearly this equation says that if you decrease the resistance, you increase the power.
  4. Aug 19, 2013 #3


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    Staff Emeritus
    Science Advisor

    Consider a circuit with a voltage of 100 volts and 10 ohms of resistance. Current through the circuit will be 10 amps and the power will be P = 100 x 10. This equals 1000 watts of power.

    Now, if we double the resistance to 20 ohms, what happens?
    Well, then it's P = 100 x WAIT!!!!
    Do we really have 10 amps still?

    If the voltage is 100 volts, and the resistance is now 20 ohms, that means that current is at 5 amps.
    So, P = 25 x 20, or 500 watts. Doubling the resistance halved the power!

    Or if we drop resistance to 5 ohms, then P = 400 x 5, or 2,000 watts. Halving the resistance doubled the power!
  5. Aug 20, 2013 #4
    Thank you very much phinds and Drakkith (I understand!) :smile:
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