Hi, I have the following question:(adsbygoogle = window.adsbygoogle || []).push({});

An A.C. voltage, V comprises of a fundamental voltage of 100V rms at a frequency of 120Hz, a 3rd harmonic which is 20% of the fundamental, a 5th harmonic which is 10% of the fundamental and at a phase angle of 1.2 radians lagging.

(1) Write down an expression for the voltage waveform

(2) The voltage at 20ms (milliseconds)

(3) Given an ideal V = 100V rms, what is the percentage error at 20ms

I have an idea for the first and second parts but I get a huge percentage error in (3) which makes me doubt whether the first 2 parts were correct, can anyone help please?

(1) Since V = Vrms x sqrt2 = 141.4V at 120Hz

3rd harmonic = 20% of 141.4 = 28.3V at 360Hz

5th harmonic = 10% of 141.4 = 14.1V at 600Hz

v = [141.1sin(240πt)] + [28.3sin(720πt] + [14.1sin(1200πt+1.2)] π=pi

(2) V at 20ms = 36.8 + 20.1 + 13.7 = 70.6V

(3) Error is [(100-70.6)/100]X100 = 29.4% !? That seems like a massive error, where has my equation gone wrong?

Help anyone!?

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# Homework Help: A.C. Voltage waveforms and harmonics?

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