rms volatge calulator – inLiteTech https://inlitetech.com Your Tech support & Navigator Sat, 24 Jul 2021 18:24:42 +0000 en-US hourly 1 https://wordpress.org/?v=6.7.2 https://inlitetech.com/wp-content/uploads/2021/06/cropped-cropped-3f2682645d8e490195ae7306fbc0f5cc-2-32x32.png rms volatge calulator – inLiteTech https://inlitetech.com 32 32 How to Calculate RMS Voltage https://inlitetech.com/calculate-rms-voltage/ https://inlitetech.com/calculate-rms-voltage/#respond Sun, 11 Jul 2021 07:42:42 +0000 https://inlitetech.com/?p=351 The RMS value is only calculated for the time-varying waveforms where the magnitude of quantity varies with respect to time.

We cannot find the RMS value for the DC waveform as the DC waveform has a constant value for every instant of time.

There are two methods to calculate RMS value.

  • Graphical Method
  • Analytical Method

Graphical Method

In this method, we use a waveform to find the RMS value. The graphical method is more useful when the signal is not symmetrical or sinusoidal.

The accuracy of this method depends on the number of points taken from the waveform. Few points result in low accuracy, and a more significant number of points result in high accuracy. 

The RMS value is a square root of the average value of the squared function. For example, let’s take a sinusoidal waveform of voltage as shown below figure.

Follow these steps to calculate the RMS voltage by graphical method.

Step-1: Divide waveform into equal parts. Here, we consider the half cycle of the waveform. You can consider full-cycle also.

The first half cycle divides into ten equal parts; V1, V2, …, V10.

Step-2: Find square of each value.

\[ V_1^2, V_2^2, V_3^2, …, V_{10}^2 \]

Step-3: Take the average of these squared values. Find the total of these values and divide by the total number of points.

\[ \frac{V_1^2+V_2^2+V_3^2+V_4^2+V_5^2+V_6^2+V_7^2+V_8^2+V_9^2+V_{10}^2}{10} \]

Step-4 Now, take square root of this value.

\[ V_{RMS} = \sqrt{\frac{V_1^2+V_2^2+V_3^2+V_4^2+V_5^2+V_6^2+V_7^2+V_8^2+V_9^2+V_{10}^2}{10}} \]

These steps are same for all type of continuous waveforms.

Analytical Method

In this method, the RMS voltage can be calculated by a mathematical procedure. This method is more accurate for the pure sinusoidal waveform.

Consider a pure sinusoidal voltage waveform defined as VmCos(ωt) with a period of T.

Where,

Vm = Maximum value or Peak value of voltage waveform

ω = Angular frequency = 2π/T

Now, we calculate the RMS value of voltage.

\[ V_{RMS} = \sqrt{\frac{1}{T} \int_{0}^{T} V_m^2 cos^2(\omega t) dt} \]
\[ V_{RMS} = \sqrt{\frac{V_m^2}{T} \int_{0}^{T} cos^2(\omega t) dt} \]
\[ V_{RMS} = \sqrt{\frac{V_m^2}{T} \int_{0}^{T} \frac{1+cos(2 \omega t)}{2} dt} \]
\[ V_{RMS} = \sqrt{\frac{V_m^2}{2T} \int_{0}^{T} 1+cos(2 \omega t) dt} \]
\[ V_{RMS} = \sqrt{\frac{ V_m^2}{2T} \left[ t + \frac{sin(2 \omega t)}{2 \omega} \right ]_0^T \]
\[ V_{RMS} = \sqrt{\frac{ V_m^2}{2T} \left[ (T-0) + (\frac{sin(2 \omega T)}{2 \omega} - \frac{sin 0}{2 \omega} ) \right ] \]
\[ V_{RMS} = \sqrt{\frac{ V_m^2}{2T} \left[ T + \frac{sin(2 \omega T)}{2 \omega} \right ] \]
\[ V_{RMS} = \sqrt{\frac{ V_m^2}{2T} \left[ T + \frac{sin(2 \frac{2 \pi}{T} T)}{2 \frac{2 \pi}{T} } \right ] \]
\[ V_{RMS} = \sqrt{\frac{ V_m^2}{2T} \left[ T +\frac{sin(4 \pi)}{2 \frac{2 \pi}{T}} \right ] \]
\[ V_{RMS} = \sqrt{\frac{ V_m^2}{2T} [T+0]} \]
\[ V_{RMS} = \sqrt{\frac{ V_m^2}{2} \]
\[ V_{RMS} = V_m \frac{1}{\sqrt{2}} \]
\[ V_{RMS} = V_m 0.7071 \]

So, RMS value of pure sinusoidal waveform can derive from the peak (maximum) value.

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]]> https://inlitetech.com/calculate-rms-voltage/feed/ 0 What is RMS Voltage? https://inlitetech.com/rms-voltage/ https://inlitetech.com/rms-voltage/#respond Sun, 11 Jul 2021 07:23:54 +0000 https://inlitetech.com/?p=349 The word RMS stands for Root Mean Square. The power of the RMS is defined as the square root of a square that means the instantaneous values ​​of an electric power signal. RMS is also known as quadratic mean. The strength of the RMS can also be explained by the continuous power varied according to the squares of rapid values ​​during the cycle.

The value of the RMS is very important in the case of an AC signal. Because the fastest amount of AC signal varies continuously with time. Unlike the DC signal, which is permanent.
Therefore, the immediate amount of electrical energy cannot be used directly in the calculation.

RMS power is also known as equivalent DC power because the RMS value gives the amount of AC power drawn by the bond as the power generated by the DC source.

For example, take a 5Ω load connected to a 10V DC source. In the case of a DC source, the amount of electrical energy remains present throughout the period. Therefore, the gravitational force is easily calculated, and is 20W.

But instead of a DC source, we use an AC source. In this case, the amount of electrical energy varies with time, as shown in the figure below.

The AC signal is a sinusoidal wave signal in most cases, as shown in the figure above. Since in a sinusoidal wave signal the interval value varies, we cannot use a quick value to calculate the force.

But if we find the RMS signal value above, we can use it to gain power. Suppose the RMS value is 10Vrms. Power dissipation per load is 20W.

The energy we get at home is the power of the RMS. Multimeters also provide an RMS value of AC power. And in the power system, we use system power which is also a valuable RMS.

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