Fundamental Electrical and Electronic Principles, Third Edition

Alternating Quantities 223A(a)All four waveforms have the same value of ω 628 rad/s, so they are all ofthe same frequency, henceω2πf628628so, f Hz2πand, f 100Hz Ansfor v , φ π/ 6 rad or 30; and V 0 V Ans1 1 m 1for v , φ π/ 3 rad or 60; and V 8V Ans2 2for v , φ π / 4 rad or 45; and V m 12 V Ans3 3m(b)Firstly the phasor diagram (Fig. 6.31 ) is sketched, very roughly to scale. Inorder to do this a reference waveform needs to be selected, and since thecurrent has a zero phase angle, this is chosen as the reference. However, if thecurrent waveform had not been specified, the horizontal axis would still betaken as the reference from which all phase angles are measured. Since v 2 andv 3 have positive phase angles, and phasors rotate anticlockwise, then thesetwo phasors will appear above the reference axis. The voltage v 1 , having anegative phase angle will appear below the reference axis. Also shown on thephasor diagram are the horizontal and vertical components of each voltage.8 V12 V/3/6/4I m (ref)10 VFig. 6.31H.C. 12 cos π/ 48 cos π/ 310 cos π/6( 12 0. 707) ( 8 0. 5) (100. 866)8. 4848.66so, H.C. 21.44 VV.C. 12 sin π/ 48 sin π/ 310sin π/ 6( 120. 707) ( 80. 866) ( 100.5)8. 486.9285and V.C. 10. 4 12VThe phasor diagram for H.C. and V.C., and the resultant phasor sum is Fig. 6.32 .