Chapt ha e pt r e r 12 RL Circuits

Transcription

1 Chapter 12 RL Circuits

2 Sinusoidal Response of RL Circuits The inductor voltage leads the source voltage Inductance causes a phase shift between voltage and current that depends on the relative values of the resistance and the inductive reactance

3 Illustration of sinusoidal response with general phase relationships of V R, V L, and I relative to the source voltage. V R and I are in phase; V R lags V S ; and V L leads V S. V R and V L are 90º out of phase with each other.

4 Relationships of the Current and Voltages in a Series RL Circuit Resistor voltage is in phase with the current Inductor voltage leads the current by 90 There is a phase difference of 90 between the resistor voltage, V R, and the inductor voltage, V L

5 Phase relation of current and voltages in a series RL circuit VL, XL Z, Vs Phase Angle I, R Reference

6 Impedance and Phase Angle of Series RL Circuits Impedance of any RL circuit is the total opposition to sinusoidal current and its unit is the ohm The phase angle is the phase difference between the total current and the source voltage The impedance of a series RL circuit is determined by the resistance (R) and the inductive reactance (X L )

7 Impedance of a series RL circuit

8 The Impedance Triangle The impedance magnitude of the series RL circuit in terms of resistance and reactance: Z = R 2 + X 2 L The magnitude of the impedance (Z) is expressed in ohms The phase angle is: θ = tan -1 (X L /R)

9 The Impedance Triangle In ac analysis, both R and X L are treated a phasor quantities, with X L appearing at a +90 angle with respect to R θ is the phase angle between applied voltage and current

10 Ohm s Law Application of Ohm s Law to series RL circuits involves the use of the phasor quantities Z, V s, and I tot V s = I tot Z I tot = V s /Z Z = V s /I tot

11 Illustration of how the variation of impedance affects the voltages and current as the source frequency is varied. The source voltage is held at a constant amplitude

12 Observing changes in Z and X L with frequency by watching the meters and recalling Ohm s law

13 Variation of Impedance and Phase Angle with Frequency Inductive reactance varies directly with frequency Z is directly dependent on frequency Phase angle θ also varies directly with frequency 0 = Purely Resistive

14 As the frequency increases, the phase angle θ increases.

15 Parallel RL Circuits - Skip

16 Power in RL Circuits When there is both resistance and inductance, some of the energy is alternately stored and returned by the inductance and some is dissipated by the resistance The amount of energy converted to heat is determined by the relative values of the resistance and the inductive reactance The Power in the inductor is reactive power: P r = I 2 X L

17 Power Triangle for RL Circuits The apparent power (P a ) is the resultant of the true power (P true ) and the reactive power (P R ) Recall Power Factor: PF = cos θ

18 Significance of the Power Factor Many practical loads have inductance as a result of their particular function, and it is essential for their proper operation Examples are: transformers, electric motors and speakers A higher power factor is an advantage in delivering power more efficiently to a load Recall Power Factor: PF = P TRUE /P A PF = R T /Z PF = cos θ

19 Illustration of the effect of the power factor on system requirements such as source rating (VA) and conductor size.

20 RL Lag Circuit (Low Pass Filter)

21 Illustration of how the frequency affects the phase lag and the output voltage in an RL lag network with the amplitude of V in held constant.

22 RL Lead Circuit (High Pass Filter)

23 Illustration of how the frequency affects the phase lead and the output voltage in an RL lead network with the amplitude of V in held constant.

24 RL Circuit as a Low-Pass Filter An inductor acts as a short to dc As the frequency is increased, so does the inductive reactance As inductive reactance increases, the output voltage across the resistor decreases A series RL circuit, where output is taken across the resistor, finds application as a low-pass filter Cutoff Frequency (f c ) is where the output voltage is R at 70.7% of its maximum value => f c = 2π L

25 Example of low-pass filtering action. As the input frequency increases, the output voltage decreases.

26 RL Circuit as a High-Pass Filter For the case when output voltage is measured across the inductor At dc, the inductor acts a short, so the output voltage is zero As frequency increases, so does inductive reactance, resulting in more voltage being dropped across the inductor The result is a high-pass filter Cutoff Frequency (f c ) is where the output voltage is R at 70.7% of its maximum value => f c = 2π L

27 Example of high-pass filtering action. As the input frequency increases, the output voltage increases.

28 Troubleshooting: Effect of an open coil.

29 Troubleshooting: Effect of an open resistor.

30 Troubleshooting: Effect of an open component in a parallel circuit with V s constant.