Can somebody please explain this?

Question

Can somebody please explain to me, why r.m.s voltage and not the average voltage is equivalent to d.c. Can you try and explain it physically, without resorting to P=IV, I know this side of it. I just can't seem to shake the picture in my head of a line denoting the average value as being the equivalent line of a d.c voltage. Why does it need that little bit extra to be equivalent? I hope this is clear.

When I say average, I mean the average of half of a sine wave.

Answer 1

Maybe if you think as alternating current as a wave form that has peaks and valleys. Then think of direct current as a straight line since it does not alternate.

Now if you take the rms (root mean square)of the peaks and valleys of alternating current, you will get a single flat line.

The rms is a type of averaging, but it gives a better fit than just averaging the highs and lows.

Answer 2

You ask "why r.m.s voltage and not the average voltage".

The reason is that it's the average power, not just average voltage. Instantaneous power is proportional to the square of the voltage (if you ignore reactance).

So, if power is proportional to the square of the voltage: the average power is the mean of the voltage squared, and the effective voltage is the square root of the mean of the power, or voltage squared. Hence R-M-S.

Answer 3

RMS is the AC voltage, the DC equivalent is the average voltage found by multiplying the peak voltage by .637.

Answer 4

Assumming you have a sin wave AC current, if you take average, mathematically, the current is zero while the actual circuit consume energy. The best way to think is imagine RMS value as you rectify the current and take average.

Answer 5

I think the missing element is the inherent resistance of the line itself. You have to boost the power a bit to compensate for some energy lost in trasfer. This is only a slightly educated guess, but I hope it helps.