What is the RMS values of AC Current and Voltage?

Answer 1

RMS stands for Root Mean Square. Basically it's what your AC voltmeter measures. So if you have a 120 volt AC signal, what you are saying is that the measured RMS voltage of the signal is 120 volts.
The RMS voltage is a measure of the equivalent heat of a DC voltage. So a 120 volts RMS AC signal, which varies between +168 volts and -168 volts and back 60 times every second, has the same heating power that a DC voltage of 120 VDC would have.

RMS voltage divided by 0.707 equals peak to peak voltage.

Alternative Answer
Think of two types of electric saw: a circular saw and a reciprocating saw. We measure the speed of these two saws in two different ways, revolutions per second and strokes per second. Is there any way of comparing the two? Well, yes, we could describe both in terms of the length of cut they would make in the same period of time (their cutting speeds).

Following this analogy, we compare direct current and alternating current by determining the heating effect of both currents. For example, if a direct current of, say, 10 A, produces a heating effect of x joules, what value of alternating current would produce exactly the same heating effect? Well, an experiment would show that this would be 0.707 times the amplitude (peak value) of that AC current which, in this particular example, would be a little over 14 A. So, instead of specifying the current's peak value, we always specify its rms-value.

Since voltage and current are proportional to each other, we can measure voltage in the same way -i.e. Vrms = 0.707 Vmax. So, as the first answer explains, a nominal voltage of 120 V actually peaks at 168 V.

(You may ask, why not simply use an average, rather than rms value? Well, apart from the fact you wouldn't be able to compare it to DC, the average of a complete positive/negative cycle would be zero!)

Answer 2

The RMS value of an sinusoidal alternating voltage is 0.707 of the peak value. That is one half of the square root of two.

The r.m.s. value of any alternating current or voltage is the value of direct current or voltage which produces the same heating effect.

Answer 3

RMS means root-mean-square. If we have a set of current values measured in a time sequence (say, 0.1, 1, 2, 3, 2.4, 1.2, and 0), the rms value is the square root of the mean of the squares, or [average(0.1^2 + 1^2 + 2^2 + 3^2 + 2.4^2 + 0^2]^0.5, which is 1.741.

If the current can be represented by a sinusoidal expression, such as i(t) = 0.5*sin(2t), where t = time in [s]. Do an average over time will result in zero.

I have created an Excel worksheet that lists the pairs of discrete (t,i) values as a substitute for the sinusoidal expression as follows.

t [s] i [A]

.00 0.000

0.10 0.099

0.20 0.195

0.30 0.282

0.40 0.359

0.50 0.421

0.60 0.466

0.70 0.493

0.80 0.500

0.90 0.487

1.00 0.455

1.10 0.404

1.20 0.338

1.30 0.258

1.40 0.167

1.50 0.071

1.60 -0.029

1.70 -0.128

1.80 -0.221

1.90 -0.306

2.00 -0.378

2.10 -0.436

2.20 -0.476

2.30 -0.497

2.40 -0.498

2.50 -0.479

2.60 -0.442

2.70 -0.386

2.80 -0.316

2.90 -0.232

3.00 -0.140

3.10 -0.042

3.20 0.058

If I average the current from t = 0 to t = 3.1s (nearly one full cycle), I get -0.012 A, near zero. On the surface, it seems the circuit will not consume any energy, even with a resistor of a finite value (R*I^2 ~ 0), but of course we know that is not true -- the resistor will be hot. Therefore, we have devised the rms term to overcome this deficiency. However, once I use the rms value for the current, I am forced to use the rms value for the voltage as well or the result will be nonsensical.

For the case of a sinusoidal expression, the rms definition will involve calculus. It is too cumbersome to do the integral of i(t) using a text editor, so I am referring the reader to the wikipedia:

Answer

Imagine trying to compare the speed of a jigsaw and a circular saw. One reciprocates, while the other rotates. The best way is by comparing the speed at which each cuts timber -as this is common to both types of saw. We use a similar techique when we want to compare a.c. and d.c. currents; we compare them by amount of work they do. The a.c. current that does exactly the same amount of work as a given d.c. current is called its root-mean-square (r.m.s.) value. So an a.c. current of, say, 5 A will do precisely the same amount of work as 5 A d.c. For a sinusoidal waveform, the r.m.s. value of current is 0.707 times its peak value (so for the previous example, the peak value of 5 A (r.m.s.) is about 7 A. Since voltage and current are proportional to each other, the r.m.s. value of any voltage is also 0.707 times its peak value. Unless otherwise specified, ALL a.c. currents and voltages are expressed in r.m.s. values.

Answer 4

The RMS voltage in India is 220V but the peak voltage may go a lot higher. A 10V rms gives a peak of about 15-16V (my observation from a transformer i used) so the peak voltage should be about 330-350V while rms is 220V or in possibly based on my observations as it was a 220V to 12V transformer with 10A output giving an rms of 10V taking the same ratio the rms at our mains should be 183V. If it is indeed 183V and not 220V then peak would be 275V.

So it should be either of the two cases below based on what actually happened

If transformer I used was in reality 10V and not 12V

RMS at mains-220V

peak-330V-350V

If transformer was perfect and it was actually due to actual mains voltage

RMS at mains-183.333V

peak-275V-303.333V

Answer 5

by dividing the peak voltage by the square root of 2, or about 1.414.

Answer 6

.707

Answer 7

Im/1.414