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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:
    • Where V = 0.707Vm and where 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:
    • Where V = 0.707Vm and where 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:
    • Where V = 0.707Vm and where 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 waveform and Phasor 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 waveform and Phasor 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 waveform and Phasor 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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