# 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)
– user16222
Nov 12, 2015 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, 2015 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. Nov 12, 2015 at 19:36

Image source: Electrical4U - Full Wave Rectifier: What is it?

This image shows your center-tapped transformer in a full wave rectifier. Almost all AC voltages are given in Vrms. Why? Because electrical engineers want one voltage, whether it's AC or DC, to represent the same amount of power to a purely resistive load. It keeps things simple.

Power = V^2/R. So, to determine the power that an AC or DC voltage delivers you have to square it. For DC that is simple. For AC it is less simple.

For AC we need only analyze a quarter of a cycle. The other three quarters deliver the same power.

We need to slice the sin wave vertically into equal time slices and find the voltage of each slice right up to the maximum, Vpeak. Then we square each of those voltages (POWER!). Add up all those squares and divide by the number of slices. That gives you the average (mean) size of all those squares. Now, take the square root of that "average" square and you get the voltage that "makes" it. That voltage is the root of the mean square, hence the name. For our particular sin wave with some peak value, we now have the DC-equivalent-power AC voltage.

Now, if you put a big capacitor across the output to smooth out the DC signal, your AC Vrms will not give you an equivalent DC voltage. In fact, once you deviate from a sin wave or from a purely resistive load, all bets are off. You'll have some additional calculating to do!