# Is Vac equivalent to Vrms?

A full wave rectifier has a 12V ac transformer (center transformer) and a 12kohm load resistor. Determine the dc load voltage and current values for the circuit?

I'm really confused. What does 12V ac transformer mean? Is it the voltage at secondary windings or primary windings? or is it the Vrms? Please explain Vrms as well.

• the general convention when dealing with AC... unless otherwise stated, the value is RMS. In 3phase system the value given is almost always given as line-line 3phase (NOTE: one exception is aerospace where the 3phase voltage is rms: phase-N) – JonRB Nov 12 '15 at 10:16

The word 'determine' sounds like you're answering a set question.

In that case, you can assume that 'Vac' and 'Vrms' mean the same thing.

You can also assume that 12v is the output of the transformer that is being input to your rectifier.

I'm not sure I know what a 'centre transformer' is. It could be a 'centre-tapped transformer', in which case the 12v winding is actually two 6v windings in series. Usually the centre tap is connected to ground, so that the two 6v outputs swing in anti-phase to allow making a full-wave rectifier easier. From the rest of the question, it looks to be irrelevant whether the transformer has a centre tap.

In AC, the voltage varies from moment to moment, so there is no such thing as the 'voltage', only v(t), the voltage as a function of time.

That is more detail than most people need.

For many purposes, we instead use Vrms, which is the value of a DC voltage that would have the same heating power when connected to a resistor. If v(t) is cos(2.pi.f.t), then the peak voltage is 1, but the rms voltage is 0.7071. Beware the difference when rectifying it, as it's the peak that makes the diodes conduct.

That ratio only holds for a pure sine wave. In many cases, the waveform is not quite sine, and the peak/rms ratio is slightly different. In some cases, square waves for instance, the ratio is quite different.

Be warned that most cheap multimeters actually read average(absolute(v(t)), which is much easier to read than rms, and then scale the result to read rms. For a pure sinewave, this scaling will be correct. For a distorted waveform, it will increase the error of the reading.

• So whenever there's Vac mentioned I can take it as Vrms? – Zeb Nov 12 '15 at 19:16
• You can probably take it as Vrms. If something else is meant, it is usually specified, so peak, or peak to peak. The one time this generalisation is false is the one time it will matter, so check if it will matter. – Neil_UK Nov 12 '15 at 19:36