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ELECTRIC CIRCUIT ANALYSIS - I. Chapter 15 – Series & Parallel ac Circuits Lecture 19 by Moeen Ghiyas. TODAY’S lesson. Chapter 15 – Series & Parallel ac Circuits. Today’s Lesson Contents. (Series ac Circuits) Impedance and Phasors Diagram Series Configuration.

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Electric circuit analysis i

ELECTRIC CIRCUIT ANALYSIS - I

Chapter 15 – Series & Parallel ac Circuits

Lecture 19

by MoeenGhiyas


Today s lesson

TODAY’S lesson

Chapter 15 – Series & Parallel ac Circuits


Today s lesson contents

Today’s Lesson Contents

  • (Series ac Circuits)

  • Impedance and Phasors Diagram

  • Series Configuration


Impedance and the phasor diagram

IMPEDANCE AND THE PHASOR DIAGRAM

  • Resistive Elements- For the purely resistive circuit,

  • Time domain equations:v = Vm sin ωt and i = Im sin ωt

  • In phasor form:

    • WhereV = 0.707Vmandwhere I = 0.707Im

  • Applying Ohm’s law and using phasor algebra, we have

  • Since i and v are in phase, thus, θR = 0°, if phase is to be same.

  • Thus, we define a new term, ZR as impedance of a resistive element (which impedes flow of current)


Impedance and the phasor diagram1

IMPEDANCE AND THE PHASOR DIAGRAM

  • Inductive Reactance- For the inductive circuit,

  • Time domain equations:v = Vm sin ωt and i = Im sin ωt

  • In phasor form:

    • WhereV = 0.707Vmandwhere I = 0.707Im

  • Applying Ohm’s law and using phasor algebra, we have

  • Since i lags v by 90°, thus, θL = 90°, for condition to be true.

  • Thus, we define term, ZL as impedance of an inductive element (which impedes flow of current)


Impedance and the phasor diagram2

IMPEDANCE AND THE PHASOR DIAGRAM

  • Capacitive Reactance- For a capacitive circuit,

  • Time domain equations:v = Vm sin ωt and i = Im sin ωt

  • In phasor form:

    • WhereV = 0.707Vmandwhere I = 0.707Im

  • Applying Ohm’s law and using phasor algebra, we have

  • Since i leads v by 90°, thus, θC = –90°, for condition to be true.

  • Thus, we define term, ZC as impedance of a capacitive element (which impedes flow of current)


Impedance and the phasor diagram3

IMPEDANCE AND THE PHASOR DIAGRAM

  • However, it is important to realize that ZR is not a phasor, even though the format is very similar to the phasor notations for sinusoidal currents and voltages.

  • The term phasor is basically reserved for quantities that vary with time, whereas R and its associated angle of 0° are fixed, i.e. non-varying quantities.

  • Similarly ZL and ZC are also not phasor quantities


Impedance and the phasor diagram4

IMPEDANCE AND THE PHASOR DIAGRAM

  • Example – Find the current i for the circuit of fig. Sketch the waveforms of v and i.

  • Solution:

  • In phasor form

  • From ohm’s law

  • Converting to time domain


Impedance and the phasor diagram5

IMPEDANCE AND THE PHASOR DIAGRAM

  • Sketch of waveformandPhasor Diagram


Impedance and the phasor diagram6

IMPEDANCE AND THE PHASOR DIAGRAM

  • Example – Find the voltage v for the circuit of fig. Sketch the waveforms of v and i.

  • Solution:

  • In phasor form

  • From ohm’s law

  • Converting to time domain


Impedance and the phasor diagram7

IMPEDANCE AND THE PHASOR DIAGRAM

  • Sketch of waveformandPhasor Diagram


Impedance and the phasor diagram8

IMPEDANCE AND THE PHASOR DIAGRAM

  • Example – Find the voltage v for the circuit of fig. Sketch the waveforms of v and i.

  • Solution:

  • In phasor form

  • From ohm’s law

  • Converting to time domain


Impedance and the phasor diagram9

IMPEDANCE AND THE PHASOR DIAGRAM

  • Sketch of waveformandPhasor Diagram


Impedance and the phasor diagram10

IMPEDANCE AND THE PHASOR DIAGRAM

  • Impedance Diagram- For any network,

    • Resistance is plotted on the positive real axis,

    • Inductive reactance on the positive imaginary axis, and

    • Capacitive reactance on the negative imaginary axis.

  • Impedance diagram reflects the individual and total impedance levels of ac network.


Impedance and the phasor diagram11

IMPEDANCE AND THE PHASOR DIAGRAM

  • Impedance Diagram

  • The magnitude of total impedance of a network defines the resulting current level (through Ohm’s law)

  • For any configuration (series, parallel, series-parallel, etc.), the angle associated with the total impedance is the angle by which the applied voltage leads the source current.

  • Thus angle of impedance reveals whether the network is primarily inductive or capacitive or simply resistive.

  • For inductive networks θT will be positive, whereas for capacitive networks θT will be negative, and θT will be zero for resistive cct.


Series configuration

SERIES CONFIGURATION

  • Overall properties of series ac circuits are the same as those for dc circuits

  • For instance, the total impedance of a system is the sum of the individual impedances:


Series configuration1

SERIES CONFIGURATION

  • EXAMPLE - Determine the input impedance to the series network of fig. Draw the impedance diagram.

  • Solution:


Series configuration2

SERIES CONFIGURATION

  • EXAMPLE - Determine the input impedance to the series network of fig. Draw the impedance diagram.

  • Solution:


Series configuration3

SERIES CONFIGURATION

  • Current is same in ac series circuits just like it is in dc circuits.

  • Ohm’s law applicability is same.

  • KVL applies in similar manner.

  • The power to the circuit can be determined by

  • where θT is the phase angle between E and I.


Series configuration4

SERIES CONFIGURATION

  • Impedance Relation with Power Factor

  • We know that

  • Reference to figs and equations

    • θT is not only the impedance angle of ZT but also θT is the phase angle between the input voltage and current for a series ac circuit.

Impedance Diagram

Phasor Diagram

Note: θT of ZT is with reference to voltage unlike FP . Also current I is in phase with VR, lags the VL by 90°, and leads the VC by 90°.


Series configuration5

SERIES CONFIGURATION

  • R-L-C Example

  • Step 1 – Convert Available information to Phasor Notation


Series configuration6

SERIES CONFIGURATION

  • R-L-C Example

  • .Step 2 – Find ZT and make impedance diagram


Series configuration7

SERIES CONFIGURATION

  • R-L-C Example

  • Step 3 – Find I or E


Series configuration8

SERIES CONFIGURATION

  • R-L-C Example

  • Step 4 – Find phasor voltages across each element


Series configuration9

SERIES CONFIGURATION

  • R-L-C Example

  • I =

  • VR =

  • VL =

  • VC =

  • .Step 5 – Make phasor diagram and

  • . apply KVL (for verification or if req)

Note: Current I in phase with VR, lags the VL by 90°, and leads the VC by 90°


Series configuration10

SERIES CONFIGURATION

  • R-L-C Example

  • Step 6 – Convert phasor values to time domain


Series configuration11

SERIES CONFIGURATION

  • R-L-C Example

  • Step 7 – Plot all the voltages and the current of the circuit


Series configuration12

SERIES CONFIGURATION

  • R-L-C Example

  • Step 8 – Calculation of total power in watts delivered to the circuit

  • or

  • or


Series configuration13

SERIES CONFIGURATION

  • R-L-C Example

  • Step 9 – The power factor of the circuit is

  • or


Summary conclusion

Summary / Conclusion

  • (Series ac Circuits)

  • Impedance and Phasors Diagram

  • Series Configuration


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