Vrms=sqrt[1/T * integral(v^2(t)dt, 0,t]
Irms=sqrt[1/T * integral(i^2(t)dt, 0,t]
RMS power is Peak-To-Peak power divided by the square root of 2.This definition, however, only holds true for a non-reactive, or resistive, load, with a power source that is truly sinusoidal.
excitation voltage is sinusoidal because it is taken from the terminal of alternator but excitation current is non-sinusoidal because it always dc.
You can work this out yourself. For a sinusoidal waveform the rms value is 0.707 times the peak value. As you quote a peak-to-peak value, this must be halved, first. Incidentally, the symbol for volt is 'V', not 'v'.
General formula: square root of the square modulus averaged over a period:xRMS =1/T sqrt( integral (|x(t)|2dt) ) ,where x(t) is the signal and T is its period.If you solve it for sinusoidal waves, you get a 1/sqrt(2)~0.707 factor between peak amplitude and RMS value:xRMS ~ 0.707 XPK ~ 0.354 XPK-PK ~ ...
The peak of a waveform that is purely sinusoidal (no DC offset) will be RMS * sqrt(2). This is the peak to neutral value. If you are looking for peak to peak, multiply by 2.
sinusoidal vs non sinusoidal
RMS power is Peak-To-Peak power divided by the square root of 2.This definition, however, only holds true for a non-reactive, or resistive, load, with a power source that is truly sinusoidal.
excitation voltage is sinusoidal because it is taken from the terminal of alternator but excitation current is non-sinusoidal because it always dc.
You can work this out yourself. For a sinusoidal waveform the rms value is 0.707 times the peak value. As you quote a peak-to-peak value, this must be halved, first. Incidentally, the symbol for volt is 'V', not 'v'.
Hi, RMS is voltage X .707 and the power is voltage X current. Hope that helps, Cubby
Rms is watts that's the amount of watts a speaker is rated for.
General formula: square root of the square modulus averaged over a period:xRMS =1/T sqrt( integral (|x(t)|2dt) ) ,where x(t) is the signal and T is its period.If you solve it for sinusoidal waves, you get a 1/sqrt(2)~0.707 factor between peak amplitude and RMS value:xRMS ~ 0.707 XPK ~ 0.354 XPK-PK ~ ...
The peak of a waveform that is purely sinusoidal (no DC offset) will be RMS * sqrt(2). This is the peak to neutral value. If you are looking for peak to peak, multiply by 2.
The root mean square (RMS) voltage is 0.707 times the peak voltage for a sinusoidal waveform because of the mathematical relationship between peak and RMS values. The RMS value is calculated as the peak value divided by the square root of 2 for a sinusoidal waveform. This factor of 0.707 ensures that the average power delivered by the AC voltage is the same as the equivalent DC voltage for resistive loads. This relationship is crucial for accurately representing and analyzing AC voltage in electrical systems.
In electricity, the root mean square (RMS) value is calculated by taking the square of the instantaneous values of a waveform over a complete cycle, averaging those values, and then taking the square root of that average. For a sinusoidal waveform, the RMS value can also be determined by multiplying the peak voltage (V_peak) by 0.707 (or 1/√2). This factor represents the ratio of the RMS value to the peak value for sinusoidal signals, where the RMS value effectively represents the equivalent DC value that would produce the same power in a resistive load.
used as wave form generators like sinusoidal and non sinusoidal,
The "effective" value of an alternating voltage is generally considered to be the RMS (Root-Mean-Square) value. The best way to measure that is with a True RMS voltmeter. Lacking that, if the voltage is sinusoidal, you can use an older style peak measuring voltmeter that estimates RMS value by dividing internally by the square root of 2. Any other shaped waveform will be measured incorrectly, depending on the amount of deviation from sinusoidal. (Square wave is the best example of error in this case - RMS and peak should be the same, but they won't read the same except on a True RMS voltmeter.)