Which one is correct for this power consumption estimation?

Question

If a MOSFET gate driver is supplied by a 12V DC power supply and if it is drawing a current I(t) from the power supply, what can we say about the power consumption in terms of voltage and current?

I was thinking the power consumption would be:

P = Vrms x Irms = 12 x Irms

But I saw some calculates as:

P = Vdc x Iavg = 12 x Iavg

Which one is correct? Why?

Which one is convenient here to calculate? The average power consumption or rms power consumption? I'm a bit confused about which one relates what.

Answer 1

The correct way to measure power consumption when the supply voltage is DC (and constant) is to multiply the voltage by the average current and forget about trying to use RMS current because that would give an incorrect answer.

If you consider that the current might be a sine wave superimposed on a DC current (just as an example) and you multiplied each individually by the DC voltage, you would get two numbers where one was the average power (the right answer) and the other is another sinewave (Vcc times higher in amplitude) whose average power value was zero hence, that second number does not contribute to average power.

Answer 2

Properly speaking, average power is calculated as:

But as you know, V(t) is constant, so we can take it away from the integral:

And as you know, that remaining integral is equal to the average current.

Hence, you can calculate it as

Bear in mind though that you can't say:

Last eqution is wrong and can't be used, because the original integral is not equal to the average of voltage times the average of current. You can do this because voltage is constant.