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AS Level     Basics     Kirchoff     >RMS<     Thevenin    

Basics RMS


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Root Mean Square

In AC circuits, measurements are usually in RMS instead of Peak.
230 Volts RMS Alternating Current (AC) has the same heating effect as 230 Volts Direct Current (DC).

RMS   =   Root Mean Square

Alternating voltages (sine waves) have an average voltage of zero because they spend equal times above and below the zero volt line.
Clearly it's not useful to say the AC mains supply voltage is zero.

For Voltage, the RMS calculation works like this.

Vrms    =   Vpeak / √2   ≈   0.707 Vpeak   ≈   0.7 Vpeak

Vpeak   =   √2 Vrms   ≈   1.414 Vrms   ≈   1.4 Vrms

For Current, the RMS calculation works like this.

Irms    =   Ipeak / √2   ≈   0.707 Ipeak   ≈   0.7 Ipeak

Ipeak   =   √2 Irms   ≈   1.414 Irms   ≈   1.4 Irms

 

The mains supply in Europe is 230 Volts RMS. The peak voltage is 325 Volts and the peak-to-peak voltage is 650V.

RMS and Peak AC Voltages

Power

P   =   E / t   =   I V   =   V2 / R   =   I2 R        Use RMS values if you need RMS power.

RMS Power Calculation

Prms = 0.5 Ppeak

Ppeak = 2 Prms

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