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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)

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