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I'm struggling to understand the reason why I'm getting different results with two apparently similar ways to compute the power consumption (over multiple time intervals) of an electrical circuit.

Let's assume I have a DC circuit with one power supply and one 10-ohms resistor. During the first 3 seconds the voltage is 5V. Then, during 1 second the voltage is 3V. I want to compute the average power over both intervals. Next, I describe both ways to compute the power that I was using:

1) P1 = V1 * V1/R = 5 * 5/10 = 2.5W
   P2 = V2 * V2/R = 3 * 3/10 = 0.9W
   Pavg = 3/4 * P1 + 1/4 * P2 = 2.1W

2) Vavg = 3/4 * V1 + 1/4 * V2 = 4.5
   Pavg  = Vavg * Vavg/R = 4.5 * 4.5/10 = 2.025W

I guess I'm missing something in here... Actually, I'm not even sure which method is the correct one (2.1W vs 2.025W). I would really appreciate it if anyone could point out what I'm doing wrong.

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The mistake comes from averaging V and then squaring the average. If you squared the voltages and then found the weighted average of the squares, the result would match your initial calculation.

There is another, more basic way to calculate the average power. Find the energy released during each of the two periods; add the two amounts of energy and divide by the elapsed time.

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  • $\begingroup$ Thanks! I guess if I only have available the values for the average voltage along intervals, there is no way to infer the real power consumption (the 2.1W), right? $\endgroup$
    – betabandido
    Commented Feb 21, 2014 at 22:26
  • $\begingroup$ True; consider an average 10 V from either a constant 10 V, or 0 V for half the time, and 20 V for the other half... $\endgroup$
    – DJohnM
    Commented Feb 21, 2014 at 23:00

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