Topic4_AC_Theory

Alternating Current Theory Topic 4 Electrical and Electronics Principles 1 1. Fleming’s Left and Right Hand Rules Fig. 1 (Left Hand Rule) Fig. 2 (Right Hand Rule) Motor Generator 2 2. Faraday’s Laws in Electromagnetic Induction Faraday’s First Law : A coil situated in a magnetic field will have an e.m.f. induced in it if the magnetic flux linking with the coil changes. Faraday’s Second law: The magnitude of the induced e.m.f. is proportional to the rate of change of magnetic flux . It is found to be proportional to the number of turns of the coil, i.e. e=−N dΦ dt =−L di dt Unit: Volts (V). 3 3. Alternating Waveform Fig. 3(a) Fig. 3(b) 4 3. Alternating Waveform Fig. 3(c) Fig. 3(d) 5 3. Alternating Waveform (a) Coil position Fig. 4 (b) Induced coil voltage versus angular position 6 3. Alternating Waveform Fig. 5 7 4. Basic Sine Wave Equation Consider a coil rotates at an angular velocity ω rad/s anti- clockwise in a fixed magnetic field. The e.m.f. produced is α = ωt (a) End view of ac generator Fig. 6 e = Emsinα (b) Voltage waveform 8 5. A Model of Dynamo (DC Generator) Fig. 7 9 6. Current Variation Over One Cycle in Dynamo + • + • Fig. 8 10 7. Definitions (Single Phase Periodic AC Waveform) Fig. 9 11 7. Definitions Cycle - one complete revolution of the rotator. Frequency, f - it is the number of cycles performed in one second and is measured in Hertz (Hz). Period, T - it is the time for one complete cycle and is measured in seconds and is given by T = 1/f. Peak value (or maximum value) - the amplitude of the waveform and always donates as Vm (Vp) or Im (Ip). Peak-to-peak value, Vp-p - the vertical distance between the positive and negative peaks. 12 7. Definitions Angle of Rotation, θ - it is the angle pass through respective to the starting point. (Unit: degree or radian) Angular Velocity, ω - it is the angle per unit time of traveled (rad/s), i.e. ω = θ / t = 2πf Instantaneous value, - the values of the voltage and/or current at any instant of time, e.g. i = Imsin(θ ± φ) A or i = Imsin(ωt ± φ) A or i = Imsin(2πft ± φ) A. Leading or Lagging angle, φ - angle reference to the origin or the starting point. 13 7. Definitions Average Value (Mean Value), avg - it is the sum of ‘n’ currents/voltages divide by ‘n’ in half cycle. π V avg ∫ 0 = V m sinθdθ = V m π ∫ sinθdθ= V m [−cosθ π ] 0 2V m = =0.636V m π−0 π 0 π π Effective Value (RMS Value), rms - it is the equivalent d.c. value which would have the same heating effect in a resistance. I rms 1 = T ∫ I 2 m sin 2 1 θdt= T ∫ I 2 m (1−cos2θ) I dt= 2 m I = m =0.707I m T 0 T 0 2 2 2 14 7. Definitions form factor = r.m s value I = rms averagevalue I avg peak factor = peakvalue r.m.s value = I I max rms Calculate the form factor and peak factor for a pure sine wave. 15 Example 1 & 2 1. The current produced by an a.c. generator has a peak value of 20 A. Calculate the instantaneous value of the current when the coil is30° past the vertical axis of the magnetic field. 2. An alternating current waveform has a period of 10 ms. Calculate its frequency. 16 Example 3 An alternating current waveform has a peak value of 5 A and a frequency of 50Hz. Calculate the valueof instantaneous current after 2.5 ms. 17 Example 4 An alternating e.m.f. is given by e = 25 sin 628t V, calculate the e.m.f. after 2 ms. What are the values of Vm, f, T and ω? 18 8. Phasor Diagram Magnitude - the amplitude of the waveform. It can be represented the Peak value or r.m.s. value. Phase angle - angle to the horizontal (or called phase difference). Reference phasor - horizontal phasor. Leading and Lagging - it is considered by anti-clockwise rotating direction. 19 9. Sine Wave in Terms of Phasor Diagram Fig. 10 20 9. Sine Wave in Terms of Phasor Diagram Fig. 11 21 Example 5 Two a.c. voltages, v1 and v2 have peak values of 20 V and 30 V respectively. If v2lags v1by 30°, draw their phasors representation by using (a) v1 as the reference, (b) v2 as the reference. Determine the supply voltage from the above two voltages. Note: More questions in Exercise 4 22 End of Topics 4 AC Theory 23 Slide Number 1 Slide Number 2 Slide Number 3 Slide Number 4 Slide Number 5 Slide Number 6 Slide Number 7 Slide Number 8 Slide Number 9 Slide Number 10 Slide Number 11 Slide Number 12 Slide Number 13 Slide Number 14 Slide Number 15 Slide Number 16 Slide Number 17 Slide Number 18 Slide Number 19 Slide Number 20 Slide Number 21 Slide Number 22 Slide Number 23