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- 1. IT2001PAEngineering Essentials (1/2)Chapter 13 – Impedance Lecturer Namelecturer_email@ite.edu.sg Sep 4, 2012Contact Number
- 2. Chapter 13 – ImpedanceLesson ObjectivesUpon completion of this topic, you should be able to: Explain and verify the characteristics of a RL and RC series circuit. Calculate the voltage, current and impedance in an AC circuit. IT2001PA Engineering Essentials (1/2) 2
- 3. Chapter 13 – ImpedanceResistive-Inductive Series Circuit Characteristics of A.C. RL Series Circuit (1) Current is in phase with VR. (2) Current lags VL by 90o. (3) Current lags VS by ϕ where ϕ is the phase angle or phase difference. IT2001PA Engineering Essentials (1/2) 3
- 4. Chapter 13 – ImpedanceResistive-Inductive Series Circuit In a resistive-capacitive circuit, the opposition to the current flow is called the impedance. Symbol : Z Unit : Ohms ( Ω ) VR = IR XL: Inductive Reactance VL = IXL VS = IZ IT2001PA Engineering Essentials (1/2) 4
- 5. Chapter 13 – ImpedanceResistive-Inductive Series Circuit Impedance Triangle of A.C. RL Series Circuit Impedance Triangle IT2001PA Engineering Essentials (1/2) 5
- 6. Chapter 13 – ImpedanceResistive-Capacitive Series Circuit Characteristics of A.C. RC Series Circuit (1) Current is in phase with VR. (2) Current leads VC by 90o. (3) Current leads VS by ϕ where ϕ is the phase angle or phase difference. IT2001PA Engineering Essentials (1/2) 6
- 7. Chapter 13 – ImpedanceResistive-Capacitive Series Circuit In a resistive-capacitive circuit, the opposition to the current flow is called the impedance. Symbol : Z Unit : Ohms ( Ω ) VR = IR Xc: Capacitive Reactance VC = IXC VS = IZ IT2001PA Engineering Essentials (1/2) 7
- 8. Chapter 13 – ImpedanceResistive-Capacitive Series Circuit Impedance Triangle of A.C. RC Series Circuit Impedance Triangle IT2001PA Engineering Essentials (1/2) 8
- 9. Chapter 13 – ImpedanceQuiz on RL Series Circuits1. An inductive circuit has a resistance of 40 ohms and an inductance of 0.2 H. It is connected to a 500 V, 50 Hz supply. Find the reactance; impedance and the current taken. (Ans: 62.8 ohms ; 74.47 ohms ; 6.71 A) XL = 2πfL Z = √ (XL2+ R2) I = V/Z = 2x3.14x50x0.2 = √62.82 + 402 = 500/74.47 = 62.8 Ω = 74.47 Ω = 6.71 A IT2001PA Engineering Essentials (1/2) 9
- 10. Chapter 13 – ImpedanceQuiz on RL Series Circuits2. An inductive circuit of resistance 16.5 ohms and inductance 0.14 H takes a current of 25 A. If the frequency is 50 Hz, find the impedance and the supply voltage. (Ans: 47 ohms ; 1175 V) XL = 2πfL Z = √ (XL2+ R2) V = IZ = 2x3.14x50x0.14 = √43.982 + 16.52 = 25x47 = 43.98 Ω = 46.98 Ω = 1175 A IT2001PA Engineering Essentials (1/2) 10
- 11. Chapter 13 – ImpedanceQuiz on RL Series Circuits3. A coil of inductance 0.45 H takes a current of 0.85 A when connected to 250 V, 40 Hz supply. What is the resistance of the coil? (Ans: 271.5 ohms) XL = 2πfL Z = V/I Z2 = (XL2+ R2) = 2x3.14x40x0.45 = 250/0.85 294.12 = 113.12 + R2 = 113.1 Ω = 294.1 Ω R = 271.5 Ω IT2001PA Engineering Essentials (1/2) 11
- 12. Chapter 13 – ImpedanceQuiz on RL Series Circuits4. An inductive circuit of resistance 4.6 ohms takes a current of 1.2 A when connected to a 220 V, 50 Hz supply. What is the inductance of the coil? (Ans: 0.583 H) Z = V/I Z2 = (XL2+ R2) XL = 2πfL = 220/1.2 183.32 = XL2 + 4.62 L = XL/2πf = 183.3 Ω XL = 183.24 Ω = 183.24/2x3.14x50 L = 0.583 H IT2001PA Engineering Essentials (1/2) 12
- 13. Chapter 13 – ImpedanceQuiz on RL Series Circuits5. A coil of inductance 0.02 H is connected in series with a resistance of 5 ohms across a supply of 200 V, 50 Hz. Find the circuit current, voltage across the resistor and inductor and the phase angle. (Ans: 24.91 A ; 124.55 V ; 156.5 V ; 51.5°) XL = 2πfL Z2 = (XL2+ R2) I = V/Z = 2x3.14x50x0.02 Z2 = 6.282 + 52 = 200/8.03 XL = 6.28 H Z = 8.03 Ω = 24.91 A VR = IR VL = IXL tan-1ϕ = XL/R = 24.91x5 = 24.91x6.28 = 156.5/124.55 = 124.55 V = 156.5 V ϕ = 51.5° IT2001PA Engineering Essentials (1/2) 13
- 14. Chapter 13 – ImpedanceQuiz on RC Series Circuits1. A capacitive reactance of 40 ohms is connected in series with a resistor of 20 ohms across a 110 V supply. Find the circuit current. (Ans: 2.46 A) Z2 = (XL2+ R2) I = V/Z Z2 = 402 + 202 = 110/44.72 Z = 44.72 Ω I = 2.46 A IT2001PA Engineering Essentials (1/2) 14
- 15. Chapter 13 – ImpedanceQuiz on RL Series Circuits2. A capacitor of 50 µF capacitance is connected in series with a resistor of 12 ohms across a 100 V, 50 Hz supply. Find the impedance, current and voltage across each component. (Ans: 64.78 ohms ; 1.54 A ; 18.53 V ; 98.29 V) Xc = 1/2πfC Z2 = (XL2+ R2) = 1/(2x3.14x50x50x10-6) Z2 = 63.662 + 122 Xc = 63.66 Ω Z = 64.78 Ω I = V/Z VR = IR VC = IXc = 100/64.78 = 1.54 x 12 = 1.54 x 63.66 = 1.54 A = 18.48 V = 98.0 V IT2001PA Engineering Essentials (1/2) 15
- 16. Chapter 13 – ImpedanceQuiz on RC Series Circuits3. A capacitive reactance of 50 ohms is connected in series with a 15 ohms resistor across a 200 V, 50 Hz supply. Calculate the impedance, current and phase angle of the circuit. (Ans: 52.2 ohms ; 3.83 A ; 73.3°) Z2 = (XC2+ R2) I = V/Z tan-1ϕ = XC/R Z2 = 502 + 152 = 200/52.2 = 50/15 Z = 52.2 Ω I = 3.83 A ϕ = 73.3° IT2001PA Engineering Essentials (1/2) 16
- 17. Chapter 13 – ImpedanceQuiz on RC Series Circuits4. A capacitive reactance of 70 ohms is connected in series with a resistance of 22 ohms across an ac supply. If the supply current is 10 A, calculate supply voltage. (Ans: 733.76 V) Z2 = (XC2+ R2) V = IZ Z2 = 702 + 222 = 10x73.376 Z = 73.376 Ω V = 733.76 V IT2001PA Engineering Essentials (1/2) 17
- 18. Chapter 13 – ImpedanceQuiz on RC Series Circuits5. A capacitor C is connected in series with a 40 ohms resistor across a supply of frequency 60 Hz. A current of 3 A flows and the circuit impedance is 50 ohms. Calculate the value of capacitance C and the supply voltage. (Ans: 88.42 µ F ; 150 V) Z2 = (XC2+ R2) V = IZ Xc = 1/2πfC 502 = XC2 + 402 = 3x50 C = 1/2πfXc XC = 30 Ω V = 150 V = 1/(2x3.14x60x30) Xc = 88.42µF IT2001PA Engineering Essentials (1/2) 18
- 19. Chapter 13 – ImpedanceSummary Phase shift, phase angle, characteristics of Resistive-Capacitive Circuit Resistive-Inductive Circuit Calculation of voltage, current and impedance in ac circuits. IT2001PA Engineering Essentials (1/2) 19
- 20. Chapter 13 – ImpedanceNext Lesson IT2001PA Engineering Essentials (1/2) 20

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