- #1
james123
Homework Statement
An A.C. voltage, V, comprises a fundamental voltage of 100V rms at a frequency of 120 Hz, 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.
- (i) Write down an expression for the voltage waveform.
(ii) Determine the voltage at 20 ms.
(iii) Given an ideal V = 100 V rms, what is the percentage error at 20 ms?
Homework Equations
Vm=Vrms*√2
V=Vm*Sin(ωt) volts
The Attempt at a Solution
(i)[/B] Vm=100*√2=141.4 volts at 120Hz
3rd Harmonic= 20% of 141.4= 141.4*0.02= 28.3 volts at 360 Hz
5th Harmonic= 10% of 141.4= 141.4*0.10= 14.1 volts at 600 HzSo, V= (141.4*Sin(240πt)) + (28.3*Sin(720πt)) + (14.1*Sin(1200πt)) ?(ii) Fundamental at 20 ms= 141.4*Sin(240πt)= 83.11 volts
3rd Harmonic at 20 ms= 28.3*Sin(720πt)= 26.91 volts
5th Harmonic at 20 ms= 14.1*Sin(1200πt)= -13.14 voltsSo, V at 20 ms= 83.11+26.91-13.14= 96.9 volts ?
(iii)
(96.9-83.11)/83.11*100= 16.59
So, percentage error at 20 ms= 16.6% ?If anyone could confirm my answers/tell me where I've gone wrong, I'd greatly appreciate it!
Many thanks in advance!