Ee1 chapter12 phasor_diagram
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  • http://www.kineticbooks.com/physics/17296/17315/sp.html The capacitor charged during one-quarter of a cycle of the current (when it went from a peak to zero), so it fully discharges during the next quarter cycle. In this quarter cycle, the current goes from zero to a maximum, but now flowing in the opposite direction
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  • 1. IT2001PAEngineering Essentials (1/2)Chapter 12 – Phasor DiagramLecturer Namelecturer_email@ite.edu.sg Sep 4, 2012Contact Number
  • 2. Chapter 12 – Phasor DiagramLesson ObjectivesUpon completion of this topic, you should be able to: Explain what is a phasor diagram. Explain and determine the characteristics of a pure resistive, pure inductive and pure capacitive circuit. 2 IT2001PA Engineering Essentials (1/2)
  • 3. Chapter 12 – Phasor DiagramPhasor Used to represent sinusoidal functions. Useful in showing the relationship Vm over time of various quantities v 2πft +φ (such as current and voltage). A phasor is a vector (i.e. described by polar coordinates length and angle) with  length equal to amplitude of function (Vm) v = Vmsin(2πft+φ)  angle equal to argument (θ)  height equal to value of function (φ) 3 IT2001PA Engineering Essentials (1/2)
  • 4. Chapter 12 – Phasor Diagram Phasor Diagram It is a diagram that represent graphically the magnitude and phase of a sinusoidal alternating current or voltage. PhasorWaveform Phase angle (ϕ) is the angle by which the voltage and current phasors are displaced with respect to each other. 4 IT2001PA Engineering Essentials (1/2)
  • 5. Chapter 12 – Phasor DiagramPhase Difference Vm1 v1 = Vm1sin(2πft+φ1) ϕ 2- ϕ 1 v2 = Vm2sin(2πft+φ2) Vm2  The two functions differ in  their amplitudes and;  their phase constants, φ1 and φ 2.  The functions have a phase difference of φ2 − φ1. 5 IT2001PA Engineering Essentials (1/2)
  • 6. Chapter 12 – Phasor DiagramPhasor Diagram There are three ways to describe the phase angle in a phasor diagram: 1. Same phase or in phase 2. Leading 3. Lagging 6 IT2001PA Engineering Essentials (1/2)
  • 7. Chapter 12 – Phasor DiagramSame Phase or In Phase V and I are in phase. The equation to represent the voltage and current waveforms are: θ=2πft v = Vm sin θ Φ=0° i = Im sin θ 7 IT2001PA Engineering Essentials (1/2)
  • 8. Chapter 12 – Phasor DiagramLeading Phase Angle I leads V by 45o. Equation: v = Vm sin θ i = Im sin (θ + 45o) 8 IT2001PA Engineering Essentials (1/2)
  • 9. Chapter 12 – Phasor DiagramLagging Phase Angle V lags I by 90o. Equation: i = Im sin θ v = Vm sin (θ - 90o ) 9 IT2001PA Engineering Essentials (1/2)
  • 10. Chapter 12 – Phasor DiagramInductor Passive electrical device that stores energy in a magnetic field, by combining the effects of many loops of electric current Change in current will induce a an opposing emf in an inductor Inductance L is a physical characteristic of an inductor (unit is Henry, H). Inductance relates the induced emf of an inductor to the rate of change of current 10 IT2001PA Engineering Essentials (1/2)
  • 11. Chapter 12 – Phasor DiagramInductors and Inductance Inductors emf opposes change in current 11 IT2001PA Engineering Essentials (1/2)
  • 12. Chapter 12 – Phasor DiagramPure Resistive CircuitCharacteristics of A.C. Pure Resistive CircuitVoltage and current are equally opposed by the circuit.The current flows through the resistor is in-phase with theapplied voltage.The phase angle between the applied voltage and current is 0° R I I V V Circuit Diagram Phasor Diagram Click next to continue 12 12 IT2001PA Engineering Essentials (1/2)
  • 13. Chapter 12 – Phasor DiagramPure Resistive Circuit The voltage across the resistor oscillates in phase with the emf of AC generator. Current and voltage across the resistor are in phase:  They peak and trough at the same time, and both are zero at the same times as well 13 IT2001PA Engineering Essentials (1/2)
  • 14. Chapter 12 – Phasor DiagramPure Resistive Circuit Sinusoidal waveform of a pure resistive circuit Applied voltage ( V ) is IN PHASE with the current ( I ) V I φ Click next to continue 14 IT2001PA Engineering Essentials (1/2)
  • 15. Chapter 12 – Phasor DiagramPure Resistive Circuit Formula for the pure resistive circuit V V V=I× R I = ---- R = ---- R I 15 IT2001PA Engineering Essentials (1/2)
  • 16. Chapter 12 – Phasor DiagramPure Inductive Circuit Characteristics of A.C. Pure Inductive Circuit There is opposition to current flow. Current flows through the pure inductor lags the applied voltage by 90°. The phase angle between the applied voltage and current is 90°. ( φ= 90° ) L : inductance in Henry ( H ) L V 90° I V I Circuit Diagram Phasor Diagram 16 16 IT2001PA Engineering Essentials (1/2)
  • 17. Chapter 12 – Phasor DiagramPure Inductive Circuit Induced emf of the inductor is oriented so it opposes the change in current. Rate of change of current determines the voltage. Current lags voltage by 90° 17 IT2001PA Engineering Essentials (1/2)
  • 18. Chapter 12 – Phasor DiagramPure Inductive Circuit Sinusoidal waveform of a pure inductive circuit Applied voltage (V ) is leading the current ( I ) by 90° V I 90° φ Click next to continue 18 18 IT2001PA Engineering Essentials (1/2)
  • 19. Chapter 12 – Phasor DiagramPure Inductive Circuit In a pure inductive circuit, the opposition to the current flow is called the inductive reactance. Symbol : XL Unit : Ohms ( Ω ) XL = 2 π f L V XL = --- f = frequency in Hertz ( Hz ) I L = inductance in Henry ( H ) Click next to continue 19 19 IT2001PA Engineering Essentials (1/2)
  • 20. Chapter 12 – Phasor DiagramPure Capacitive Circuit Characteristics of A.C. Pure Capacitive Circuit Current flows through the pure capacitor leads the applied voltage by 90°. The phase angle between the applied voltage and current is 90°. ( φ= 90° ) C = capacitance in Farad ( F ) C I I 90° V V Circuit Diagram Phasor Diagram 20 IT2001PA Engineering Essentials (1/2)
  • 21. Chapter 12 – Phasor DiagramPure Capacitive Circuit Current starts at a maximum while the voltage across the capacitor is zero, since it is initially uncharged When the current reaches zero, the capacitor plates are fully charged, and the magnitude of the voltage across it is at a maximum The current reaches a peak earlier in time than the potential difference does. Current leads voltage by 90° 21 IT2001PA Engineering Essentials (1/2)
  • 22. Chapter 12 – Phasor DiagramPure Capacitive Circuit Sinusoidal waveform of a pure capacitive circuit Current ( I ) is LEADING the Applied voltage (V ) by 90° V I 90° φ 22 22 IT2001PA Engineering Essentials (1/2)
  • 23. Chapter 12 – Phasor DiagramPure Capacitive Circuit In a pure capacitive circuit, the opposition to the voltage is called the capacitive reactance. Symbol : Xc Unit : Ohms ( Ω ) 1 V Xc = --------- Xc = --- 2π f C I f = frequency in Hertz ( Hz ) Click next = capacitance in Farad ( F ) C to continue 23 23 IT2001PA Engineering Essentials (1/2)
  • 24. Chapter 12 – Phasor DiagramQuiz 1. The diagram shows the phasor diagram of the I V A. Pure capacitive circuit B. Pure resistive circuit C. Pure inductive circuit D. Resistor-inductor series circuit Ans : B 24 IT2001PA Engineering Essentials (1/2)
  • 25. Chapter 12 – Phasor DiagramQuiz 2. The phase angle between the applied voltage and the current in an A.C. pure resistive circuit is A. 0° B. 30° C. 45° D. 90° Ans : A 25 IT2001PA Engineering Essentials (1/2)
  • 26. Chapter 12 – Phasor DiagramQuiz 3. In the pure inductive circuit the current A. Is in phase with the applied voltage B. Leads the applied voltage by 90° C. Lags the applied voltage by 45° D. Lags the applied voltage by 90° Ans : D 26 IT2001PA Engineering Essentials (1/2)
  • 27. Chapter 12 – Phasor DiagramQuiz 4. The inductive reactance is represented by an equation : A. XL = 2 f L B. XL = 2 πf L C. XL = V f L 1 D. XL = -------- 2πfL Ans : B 27 IT2001PA Engineering Essentials (1/2)
  • 28. Chapter 12 – Phasor DiagramQuiz 5. Which is the correct phasor diagram of an A.C. pure capacitive circuit?. I A. I V C V . V I B D I V . . Ans : D 28 IT2001PA Engineering Essentials (1/2)
  • 29. Chapter 12 – Phasor DiagramQuiz 6. The opposition to the current flow in a pure capacitive circuit is called A. Impedance B. Resistance C. Inductive reactance D. Capacitive reactance Ans : D 29 IT2001PA Engineering Essentials (1/2)
  • 30. Chapter 12 – Phasor DiagramQuiz7. The capacitive reactance is represented by an equation : A. Xc = 2 π C B. Xc = 2 π f C 1 C. Xc = --------- 2fC 1 D. Xc = --------- 2πfC Ans : D 30 IT2001PA Engineering Essentials (1/2)
  • 31. Chapter 12 – Phasor DiagramQuiz 8. The current flow in an A.C. pure inductive circuit can be calculated using a formula : V A. I = ---- R V B. I = ----- XL V C. I = ----- Xc D. I = V XL Ans : B 31 IT2001PA Engineering Essentials (1/2)
  • 32. Chapter 12 – Phasor Diagram Quiz9. The sinusoidal waveform V of an A.C. circuit shows I that the 90° φ A. Applied voltage is in phase B. Applied voltage is lagging with the current the current by 90° D. Current is leading the C. Applied voltage is leading applied voltage by 90° the current by 90° Ans : C 32 IT2001PA Engineering Essentials (1/2)
  • 33. Chapter 12 – Phasor Diagram Quiz10. The diagram shows an V A.C. sinusoidal waveform I of a φ A. Pure resistive circuit C. Pure capacitive circuit B. Pure inductive circuit D. Resistor-Capacitor series circuit Ans : A 33 IT2001PA Engineering Essentials (1/2)
  • 34. Chapter 12 – Phasor DiagramSummary Phasor Diagrams Phase shift, phase angle, characteristics of  Purely resistive circuit  Purely capacitive circuit  Purely inductive circuit 34 IT2001PA Engineering Essentials (1/2)
  • 35. Chapter 12 – Phasor DiagramNext Lesson 35 IT2001PA Engineering Essentials (1/2)