Which one of these transformer RMS equations is correct?

In the textbook Power Electronics Devices, Circuits & Applications 4/E by M.H. Rashid, chapter 3, page 108, I found two conflicting equations which made me really confused. The equations are indicated with yellow highlighter below:

Which one of these equations is correct? I am utterly confused by many other equations as well; the book doesn't seem to be very consistent.

• The second one is correct. I don't know the book but, by the looks of this, they are quite liberal in mixing numbers, which is not only not consistent, but potentially confusing. Either use 0.707 and 1.41 consistently, or $\sqrt2$ and $1/\sqrt2$ (or $\sqrt2^{-1}$, or $2^{-0.5}$). Maybe it's time to grab a different book? Commented Nov 15, 2022 at 8:04

That is a pretty confusing book and his definitions of efficiency etc. are quite idiosyncratic. If you're not forced to use it, maybe find another. Things like:

Diodes are extensively used in rectifiers.

He considers an ideal rectifier as a kind of a magic box that would convert AC into smooth DC while acting as a resistive load at the input.

This stuff may well be self-consistent, and it gets some useful results, but the terminology is strange and probably won't match up with other references.

I believe both equations are true, but are referring to different things. In the case of considering the entire center-tapped transformer winding the RMS current of each half is 0.707 of the total (since each delivers half the power and power is proportional to current squared) . Therefore we have $$\(0.707)^2\cdot V_M/R\$$ = 0.5Vm/R. This is important when we are looking at the transformer utilization.

Figure from the book:

• I forgot about this case but, in my defence, the example in the OP is not very clear on it and only references equations, not figures (from what I see). Also, using the same Is for both definitions is not helpful, either. Commented Nov 15, 2022 at 22:16
• @aconcernedcitizen Yes, it's poorly explained and without pulling the actual book up (which took some doing) I would have written the same comment if you hadn't gotten there first. The author strikes me as brilliant but the odd terminology suggests an alien education, maybe a power systems engineer educated in the former USSR would find it familiar. Commented Nov 16, 2022 at 1:59
• The author did his masters and PhD in the University of Birmingham. :-) Commented Nov 16, 2022 at 5:20
0.5 is the square of 0.707. So it looks like an editorial mistake (i.e. wrong number has been copied/taken) instead of a technical one but led to a grave mistake. The one marked on item f is correct.
Also, I can't understand why the transformer's VA rating is taken as $$\P_A=\sqrt2 \ V_s \ I_s \$$ instead of $$\ P_A= V_s \ I_s \$$ where $$\V_s\$$ and $$\I_s\$$ are RMS voltage and current, respectively. At item d the authors define the RMS voltage and current so RMS volts and currents are involved, but it's unclear where that $$\\sqrt2\$$ came from. The definition has no $$\\sqrt2\$$ factor, normally.