# AC voltage measurement - Vrms

• StonieJ
In summary, the VRMS of an AC triangle wave is equal to the square of the Vmax divided by the square root of the integration interval. For the sine wave, the RMS multiplier is simply the square of the Vmax.
StonieJ
I feel like I'm so close to the correct answer for this problem, but I just can't seem to bring it all together.

Code:
To find the V[sub]RMS[/sub] of an AC sine wave, you use the following
forumla, where V[sub]max[/sub] is the maximum amplitude:

V[sub]RMS[/sub] = V[sub]max[/sub] / sqrt(2)

To find the V[sub]RMS[/sub] of an AC triangle wave, you use:

V[sub]RMS[/sub] = V[sub]max[/sub] / sqrt(3)

In one sentence, give a good qualitative reason why sqrt(3) is appropriate
for the triangle wave.

I have a bunch of vague and un-elegant ideas, but not really one good sentence. I've been Googling on the subject and coming up with crest factor (peak / RMS), which is sqrt(3) for triangle waves and sqrt(2) for sine waves. But I have yet to bring it all together. Any help is appreciated.

You need to integrate the square of the wave form over one period and divide by the integration interval to find the mean square. Then you take the square root.

because in the triangle wave, V is proportional to t... and V^2 is proportional to t^2, when you do the RMS, you need to take the squreroot of $$\int V^2 dt$$, this is where the root 3 come from

Hint:

The method for calculating the "crest factor" is simple:

1) Square the function under consideration. (That's the "square" part of the term "root mean squared.")

2) Average that squared function over time; one period is enough. (That's the "mean" part.)

3) Take the square root of the result. (That's obviously the "root" part.)

For the sine wave, the RMS multiplier is thus:

$$\sqrt{\frac{\int_0^{2 \pi} \sin^2 x dx}{2 \pi}} = \frac{1}{\sqrt{2}}$$

To come up with an elegant sentence, first, recognize that $1/\sqrt{3}$ is smaller than $1/\sqrt{2}$. Next, graph the squared triangle wave superimposed over the squared sine wave. Notice that the squared sine wave is always equal to or greater than the squared triangle wave. Thus, its time average is correspondingly larger.

- Warren

## 1. What is AC voltage measurement?

AC voltage measurement is the process of determining the magnitude of an alternating current (AC) electrical signal. This is typically done using a voltmeter, which measures the voltage at a specific point in an electrical circuit.

## 2. What is Vrms?

Vrms, also known as root mean square voltage, is a type of AC voltage measurement that takes into account the varying amplitude of the AC signal. It is a measure of the effective or average voltage of an AC signal, and is used to determine the power and energy in AC circuits.

## 3. How is Vrms calculated?

Vrms is calculated by taking the square root of the mean of the squares of the instantaneous voltage values over one period of the AC signal. This accounts for the changing amplitude of the signal and provides a more accurate measurement of the voltage.

## 4. Why is Vrms important?

Vrms is important because it is a more accurate representation of the effective voltage in an AC circuit. It is used in calculations for power and energy, and is also a standard measurement used in many industries, such as electronics and power distribution.

## 5. How is AC voltage measurement different from DC voltage measurement?

AC voltage measurement is different from DC voltage measurement in several ways. In AC voltage measurement, the voltage is constantly changing direction, while in DC voltage measurement, the voltage remains constant. Additionally, AC voltage measurement requires the use of specialized equipment, such as an AC voltmeter, while DC voltage measurement can be done with a standard voltmeter. Lastly, the calculations for AC voltage measurement, such as Vrms, are more complex than those for DC voltage measurement.

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