Root Mean Square Voltage Calculator

RMS Voltage Formula:

\[ V_{rms} = \frac{V_{peak}}{\sqrt{2}} \]

RMS Voltage (V_rms):

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1. What is RMS Voltage?

The Root Mean Square (RMS) voltage is the equivalent DC voltage that would produce the same power dissipation in a resistive load. For sinusoidal waveforms, it's related to the peak voltage by a factor of 1/√2.

2. How Does the Calculator Work?

The calculator uses the RMS voltage formula:

\[ V_{rms} = \frac{V_{peak}}{\sqrt{2}} \]

Where:

\( V_{rms} \) — Root Mean Square voltage (volts)
\( V_{peak} \) — Peak voltage (volts)
\( \sqrt{2} \) ≈ 1.4142

Explanation: The RMS value is calculated by dividing the peak voltage by the square root of 2, which is approximately 1.4142.

3. Importance of RMS Voltage

Details: RMS voltage is crucial in AC circuit analysis as it represents the effective voltage that does work in a circuit. Most AC voltmeters display RMS values, and electrical ratings are typically given in RMS terms.

4. Using the Calculator

Tips: Enter the peak voltage in volts. The value must be positive. The calculator will compute the RMS voltage.

5. Frequently Asked Questions (FAQ)

Q1: Why use RMS voltage instead of peak voltage?
A: RMS voltage gives the equivalent DC voltage that would produce the same heating effect in a resistor, making it more useful for power calculations.

Q2: What's the relationship between RMS and peak-to-peak voltage?
A: For a sine wave, V_rms = V_peak-to-peak / (2√2).

Q3: Does this formula work for all waveforms?
A: No, this specific formula only applies to pure sinusoidal waveforms. Other waveforms have different conversion factors.

Q4: What's a typical RMS voltage for household AC?
A: In many countries, household AC is 120V or 230V RMS, with corresponding peak voltages of about 170V or 325V.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for ideal sine waves. Real-world measurements may vary slightly due to waveform distortion.