# How to calculate the .707 value used in rms voltage

• scoot15638
In summary, to calculate the .707 value using calculus, you can take the integral of V(t)2 over a full cycle, divide by the time of the cycle, and then take the square root of the answer. This is also known as the root mean square and is used for calculating Vrms for a sine wave. However, this value is only applicable for a sine wave and cannot be used for other waveforms.

#### scoot15638

I need help, and can't find anywhere how to calculate the .707 value using calculus. The value used when calculating Vrms =Vp*.707, i need to know how to calculate the .707. Any help would be great, Thanks!

Scott

.707 is for a sine wave only, and you could determine it by taking the integral of V(t)2 over a full cycle, dividing by the time of the cycle, and then taking the square root of the answer (hence the name "root mean square").

## 1. How is the .707 value used in RMS voltage calculated?

The .707 value used in RMS voltage is calculated by taking the square root of 2 divided by 2, or 1/√2. This value is used to convert peak voltage to RMS voltage in AC circuits.

## 2. What is the significance of the .707 value in RMS voltage?

The .707 value is significant because it represents the ratio between the peak voltage and the RMS voltage in an AC circuit. This value is used to accurately measure the effective voltage in AC circuits.

## 3. Why is the .707 value used instead of 1 in RMS voltage calculations?

The .707 value is used because it represents the average power of an AC circuit. In AC circuits, the voltage and current are constantly changing, so using the peak voltage (which is 1 in this case) would not accurately reflect the true power of the circuit.

## 4. How does the .707 value affect the measurement of voltage in AC circuits?

The .707 value is used to convert peak voltage to RMS voltage in AC circuits. This means that the voltage measured using a multimeter or other device will be multiplied by .707 to accurately reflect the effective voltage in the circuit.

## 5. Is the .707 value used in all AC circuits?

Yes, the .707 value is used in all AC circuits to convert peak voltage to RMS voltage. This is because the AC voltage is constantly changing and the .707 value represents the average power of the circuit, making it a more accurate measurement than the peak voltage.