CH12 Mine No Parallel.ppt - engineering.sdsu.edujohnston/EE204_PDF_Slides/Chapters … · Microsoft PowerPoint - CH12 Mine No Parallel.ppt [Compatibility Mode] Author: johnstonht

Chapter 12Chapter 12RL Circuits

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 reactancethe resistance and the inductive reactance

Illustration of sinusoidal response with general phase relationships of VR, V

L, and I relative to the

source voltage.

VR

and I are in phase; VR

lags VS; and V

Lleads V

S. V

Rand V

Lare 90º out of phase with each other.

Thomas L. Floyd

Electronics Fundamentals, 6e

Electric Circuit Fundamentals, 6e

Copyright ©2004 by Pearson Education, Inc.

Upper Saddle River, New Jersey 07458

All rights reserved.

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°the current by 90°

• There is a phase

difference of 90°

between the resistor

voltage, VR, and the

inductor voltage, VL

Phase relation of current and voltages in a series RL circuit

Thomas L. Floyd






I, R

VL, XL

Z, Vs

Phase Angle

Reference

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 voltagethe total current and the source voltage

• The impedance of a series RL circuit is

determined by the resistance (R) and the inductive

reactance (XL)

Impedance of a series RL circuit

Thomas L. Floyd






The Impedance Triangle

• The impedance magnitude of the series RL

circuit in terms of resistance and reactance:

Z = √R2 + X2LZ = √R2 + X2L

– The magnitude of the impedance (Z) is

expressed in ohms

• The phase angle is:

θ = tan-1(XL/R)

The Impedance Triangle

• In ac analysis, both R and XL are treated a phasor quantities, with XL appearing at a +90° angle with respect to R

• θ is the phase angle between applied voltage and current• θ is the phase angle between applied voltage and current

Ohm’s Law

• Application of Ohm’s Law to series RL

circuits involves the use of the phasor

quantities Z, Vs, and Itotquantities Z, Vs, and Itot

Vs = ItotZ

Itot = Vs/Z

Z = Vs/Itot

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

Thomas L. Floyd






Observing changes in Z and XL

with frequency by watching the meters and recalling

Ohm’s law

Thomas L. Floyd






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• Phase angle θ also varies directly with frequency

0° = Purely Resistive

As the frequency increases, the phase angle θθθθ increases.

Thomas L. Floyd






Thomas L. Floyd






Parallel RL Circuits - Skip

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 resistanceby 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:

Pr = I2XL

Power Triangle for RL Circuits

• The apparent power (Pa) is the resultant of the true

power (Ptrue) and the reactive power (PR)

• Recall Power Factor: PF = cos θ

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 = PTRUE/PA

– PF = RT/Z

– PF = cos θ

Illustration of the effect of the power factor on system requirements such as source

rating (VA) and conductor size.

Thomas L. Floyd






RL Lag Circuit (Low Pass Filter)

Thomas L. Floyd






Illustration of how the frequency affects the phase lag and the output voltage in an RL

lag network with the amplitude of Vin

held constant.

Thomas L. Floyd






RL Lead Circuit (High Pass Filter)

Thomas L. Floyd






Illustration of how the frequency affects the phase lead and the output voltage in an RL

lead network with the amplitude of Vin

held constant.

Thomas L. Floyd






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 (fc) is where the output voltage is

at 70.7% of its maximum value => L

Rfc

π2=

Example of low-pass filtering action.

As the input frequency increases, the output voltage decreases.

Thomas L. Floyd






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 zerois 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 (fc) is where the output voltage is

at 70.7% of its maximum value => L

Rfc

π2=

Example of high-pass filtering action.

As the input frequency increases, the output voltage increases.

Thomas L. Floyd






Troubleshooting: Effect of an open coil.

Thomas L. Floyd






Troubleshooting: Effect of an open resistor.

Thomas L. Floyd






Troubleshooting: Effect of an open component in a parallel circuit with Vs

constant.

Thomas L. Floyd






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CH12 Mine No Parallel.ppt - engineering.sdsu.edujohnston/EE204_PDF_Slides/Chapters … · Microsoft PowerPoint - CH12 Mine No Parallel.ppt [Compatibility Mode] Author: johnstonht