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.
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.
Anyway, in answer to your question...
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:
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.
PS: Haven't heard of that book until today. Skimmed through some reviews and an Amazon review mentions technical mistakes.
I don't think there is an error. For a pure sinusodial voltage of 1.4142 V peak the rms voltage is 1.0. Now lets divide both by 2, we get 0.7070 V peak and 0.5 V rms.
