Last Updated on October 22, 2023 by Kevin Chen

The words alternating and direct current is often used in electronics. As a result, an alternating waveform is connected to an AC. This indicates that the periodic waveform alternates between negative and positive values. A sinusoidal waveform is the most common waveform used to illustrate this.

The current and voltage values are almost always stable for direct current waveforms. The representation of stable values, as well as their magnitude values, is straightforward. However, as previously stated, the magnitude values of AC waveforms are not as straightforward as they vary continuously with time. There are several techniques for determining this, the most popular of which is “RMS Voltage.” This article discusses the complete RMS voltage theory, including its equations, methodologies, etc.

## What is RMS?

RMS stands for Root Mean Square. This is the adequate amount of power in an AC signal in terms of electricity (including audio). Because AC power is a periodic waveform with parts of its period above and below “zero,” determining how much actual power is available over time is more complicated than with DC, where the voltage and current are (nearly) constant.

The Root Mean Square approach is a widely accepted way of calculating the signal’s “heating value” – the effective voltage that would generate the same amount of heat as a DC (Direct Current) signal over the same period. The Root Mean Square value of an AC wave is frequently referred to as the practical value or DC-equivalent value in a circuit with a pure resistance impedance. If a 100-volt RMS AC source is connected across a resistor, and the associated current causes the resistor to dissipate 50 watts of heat, a 100-volt DC source attached to the resistor will also expend 50 watts of heat.

## What is the RMS Voltage?

“Root Mean Square Value” is what RMS stands for. The RMS value is the voltage of an AC signal comparable to DC voltage. Both AC and DC signals have the same power or heating effect. Because the magnitude of current and voltage values changes with time, the values of a sinusoidal signal fluctuate over time, and it is not relevant to DC circuits (magnitude constant).

It can be described as the square roots of the average values of an AC signal’s instantaneous values in simple terms. Vrms or Irms are the symbols for it. Squaring the input values and calculating the average value of an AC signal yields this result. The square voltage is calculated by taking the square root of the average value obtained.

## What is the Average Value?

Suppose we use rectifiers to convert an alternating current (AC) sine wave into a direct current (DC) sine wave. In that case, the transformed value is the average value of that alternating current sine wave.

If the greatest value of alternating current is “IMAX,” the converted DC through the rectifier will be “0.637 IM,” which is the AC Sine wave’s average value (IAV).

Average Value of Current = I_{AV} = 0.637 I_{M}

Average Value of Voltage = E_{AV} = 0.637 E_{M}

The Average Value (also known as the Mean Value) of an Alternating Current (AC) is defined as the Direct Current (DC) that carries the same amount of charge across any circuit as the Alternating Current (AC) during the same time.

Keep in mind that the average or mean value of a whole sinusoidal wave is “Zero,” which means that the value of current in the first half (Positive) equals the value of current in the next half-cycle (Negative) in the opposite direction. In other words, the positive and negative half-cycles have an equal amount of current flowing in the opposite direction; hence, the average value for a complete sine wave is “0.” That is why, when plating and charging batteries, we do not utilize the average value. When an AC wave is rectified into DC, it can be employed in electrochemical applications.

In summary, because the positive values (above the zero crossing) counteract or neutralize the negative values, the average value of a sine wave calculated over a whole cycle is always zero (below the zero crossing.)

## MS Voltage Theory

Waveforms of voltage or current are commonly used to depict AC and DC signals. We already knew that the DC signal’s magnitude is constant and simple to calculate. On the other hand, the AC signal oscillates between negative and positive half cycles and changes over time. Thus, determine the magnitude of the alternating waveform’s voltage and current values. The alternating waveform, as illustrated below, can be used to explain this principle.

Calculating the RMS Voltage value is the most efficient way to determine the magnitude of the voltage values in a sinusoidal waveform. The amount of power delivered to the load or circuit by AC and DC signals can be compared. This value is referred to as the DC equivalent voltage of an AC signal since the amount of power dissipated or the heating impact of both AC and DC waveforms in a particular circuit are the same.

The DC power given to the load is equivalent to the sine wave’s RMS voltages (AC signal). This is indicated by Veff or Ieff and gives the practical voltage value. If the supply voltage is 220V-240V, the RMS voltage values of an AC are also 220V-240V, which is the same as the DC voltage power.

The quantity of power dissipated in the circuit is the same if the RMS voltages of the AC and DC signals are the same. This is sometimes called an effective voltage, the same as the DC voltage used to power the circuit.

### Equation

The RMS Voltage Equation is more significant to understand because it is used to calculate a variety of values, and the basic equation is

V_{RMS} = V_{peak-voltage} * (1/ (√2)) = V_{peak-voltage} * 0.7071

The RMS voltage is determined by the magnitude of the AC wave and is not affected by the phase angle or frequency of the alternating current waveforms.

For example, if the peak voltage of the AC waveform is 30 volts, then the RMS voltage is computed as follows:

V_{RMS} = V_{peak-voltage} * (1/ (√2)) = 30 * 0.7071 = 21.213

The resulting value is nearly equal in both the graphical and analytical procedures. Only sinusoidal waves can cause this. The graphical technique is the only alternative in the case of non-sinusoidal waves.

We can calculate the voltage between two peak values, VP-P, instead of utilizing the peak voltage.

The values for Sinusoidal RMS are calculated as follows:

V_{RMS} = V_{peak-voltage} * (1/ (√2)) = V_{peak-voltage} * 0.7071

V_{RMS} = V_{peak-voltage} * (1/ 2(√2)) = V_{peak-peak} * 0.3536

V_{RMS} = V_{average} * (∏/ (√2)) = V_{average}* 1.11

### RMS Voltage Equivalent

The RMS voltage value of a sine wave or even a more sophisticated waveform can be calculated using two general methodologies. The methods are as follows:

### RMS Voltage Graphical Method

- This is used to determine the RMS voltage of a non-sine wave that changes over time. This can be accomplished simply by pointing the wave’s mid-ordinates.

### RMS Voltage Analytical Method

This is used to use mathematical computations to calculate the wave’s voltage.

### Graphical Approach

In this procedure, the RMS value is calculated similarly for both the positive and negative sides of the wave. As a result, this article describes how a positive cycle works. A certain amount of precision for a similarly spaced instant across the waveform can be used to calculate the value.

The positive half cycle is divided into ‘n’ equal sections, commonly known as middle ordinates. The outcome will be more accurate if there are more middle ordinates. As a result, the breadth of every middle ordinate will be n degrees, and the height will equal the wave’s instant value across the x-axis.

Every value in the wave’s middle ordinate is doubled, then added to the next value. The squared value of the RMS voltage is obtained using this method. The result is then divided by the entire number of middle ordinates, yielding the RMS voltage Mean value. As a result, the RMS voltage equation is:

Vrms = [total sum of the middle ordinates × (voltage)2]/ number of the middle ordinates

There are 12 middle ordinates in the example below, and the RMS voltage is displayed as

V_{RMS} = √(V_{1}^{2}+ V_{2}^{2}+ V_{3}^{2}+ V_{4}^{2}+ V_{5}^{2}+ V_{6}^{2}+……+ V_{12}^{2})/12

Consider alternating voltage, which has a peak voltage of 20 volts and is calculated using 10 middle ordinate values as follows:

V_{RMS} = √(6.2^{2}+ 11.8^{2}+ 16.2^{2}+ 19^{2}+ 20^{2}+ 16.2^{2}+ 11.8^{2}+ 6.2^{2}+ 0^{2})/10 = √(2000)/12

V_{RMS} = 14.14 Volts

The graphical method produces good results in determining the RMS values of an AC wave that is either sinusoidal or symmetrical. As a result, the graphical method can be used to analyze even the most complex waveforms.

### Analytical Approach

This method only works with sine waves, which are simple to obtain RMS voltage values using a mathematical approach. A periodic sine wave is constant and is written as

V_{(t) }= V_{max}*cos(ωt).

The RMS value of the Sine voltage V(t) in this case is

V_{RMS} = √(1/T ʃ^{T}_{0}V_{max}^{2}*cos^{2}(ωt))

VRMS = (1/T T0Vmax2*cos2(t)) when the integral limits are examined between 00 and 3600.

RMS voltage is the best technique for representing signal magnitude, current, and voltage values for AC voltages. The RMS value does not match the median of the entire set of instant readings. The proportion of RMS voltage to peak voltage value is the same as the proportion of RMS current to peak current value.

When accurate sine waves are considered, many multimeter instruments, whether ammeters or voltmeters, calculate RMS values; the RMS value of the non-sine wave must be measured with an “Accurate Multimeter.” The RMS value for a sine wave produces a heating effect comparable to that of a DC wave.

I2R, for example, equals IRMS2R. If AC voltages and currents are not viewed as other values, they must be considered RMS values. As a result, a 10 amp AC will produce a similar heating effect as a 10 amp DC with a peak value of 14.12 amps.

## Examples of RMS Voltage

Consider the following scenario: we have a load that we wish to dissipate no more than 0.5 watts of energy from. This is the load’s highest constant power capability. Because power= current x volts, the maximum current that can flow through this circuit if we utilize a 10-volt DC power supply is 50mA. As a result, 10V x 50mA=0.5W. Let’s pretend we wish to go from working with a DC circuit to an AC circuit.

We can take the DC example we just figured out to figure out what AC voltage we can use for this circuit without exceeding its power constraints. If we allow 50mA of current for this AC voltage, we can operate this circuit with an RMS voltage of 10VAC. If we utilize a 10V RMS voltage, the peak voltage available in this circuit is around 14.1V. RMS voltage operates like this. It enables us to work with DC circuit models and determine the right AC voltage that causes the same amount of heating or power dissipation through a load as the DC voltage. RMS values describe many different types of voltages in real life.

The voltage from an AC outlet is a good illustration. You’re undoubtedly aware that 120V is generated by an AC outlet, such as one found in your home or any other building in the United States. But you probably have no idea what voltage this is. RMS voltage is the correct answer. The RMS voltage is 120V. And the maximum voltage for this is 170V. As a result, the peak voltage of this voltage is much higher than 120V. When measured from peak to peak, the voltage from an AC outlet is 340V peak-to-peak.

It’s more accessible to relate to DC circuits by utilizing the RMS voltage, which is the voltage that comes from an AC outlet.

## Conclusion

Thus, the RMS voltage concept, its equation, sinusoidal waveforms, techniques for calculating these voltage values, and the comprehensive RMS voltage theory are all covered in this article. We hope you found this information useful in your efforts.

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