Root Mean Square: Voltages & Currents

Definition:

• The R.M.S. value of an A.C. (alternating current) signal is the equivalent value of direct current (D.C.) that would have the same effect or energy change as the A.C.

Example

• If a 12-volt car battery powers a 36-watt light bulb with D.C., an A.C. supply needs to be set at 12 V R.M.S. to achieve the same 36 W power output.

R.M.S. vs. Peak Voltage

• The R.M.S. voltage of an A.C. signal is always less than the peak voltage.
• Peak voltage occurs only twice in the cycle (once positive, once negative); the rest of the time, it is less.

R.M.S. Voltage Calculation

• To calculate R.M.S. voltage from peak voltage, use the square root of 2 (approximately 1.414).

R.M.S. vs. Peak Current

• Similar relationships exist between R.M.S. and peak current values.

Example - UK Mains Voltage

• Mains voltage in the U.K. varies between 216 and 253 volts (R.M.S. values).
• To calculate the maximum possible voltage from a mains socket, use the peak voltage for 253 volts R.M.S..

Safety Consideration

Peak Power vs. R.M.S. Power

• Peak power developed by an A.C. appliance is higher than the R.M.S. power because peak values occur briefly during the cycle.
• R.M.S. power accounts for the effective continuous power output of the appliance.