# Why does the TUF formula use $V_{rms}=\frac{V_m}{\sqrt{2}}$ and not $V_{rms}=\frac{V_m}{2}$ for a half wave rectifier

We know that for a half wave rectifier $$\V_{rms}=\frac{V_m}{2}\$$ and $$\I_{rms}=\frac{I_m}{2}\$$

But the Transformer utilization factor uses $$\V_{rms}=\frac{V_m}{\sqrt{2}}\$$ (But uses $$\I_{rms}=\frac{I_m}{2}\$$) to calculate the "ac rated power" as $$\\frac{V_m}{\sqrt{2}}*\frac{I_m}{2}\$$. Why?

• A diagram would be nice. – Transistor Jan 6 '19 at 9:35
• @Transistor For half wave rectifier? – paulplusx Jan 6 '19 at 10:19

I think I got it and it is quite silly. There are two $$\V_{rms}\$$ voltages, it can be considered as:
$$\V_{rms(input)}\$$ : The voltage that is measured before the diode i.e. at the input of the diode and it's the direct output of the transformer.
$$\V_{rms(output)}\$$ : The voltage that is measured after the diode.
Also, since it's a diode in series, the current before the diode is the same current that is after the diode hence there is only one $$\I_{rms}\$$
The AC rated power uses the $$\V_{rms(input)}\$$ which is quite obvious because that's the voltage across the secondary winding of the transformer.