- #1
alex.daciz
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Hi, I have the following question:
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!?
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!?