Nothing Special   »   [go: up one dir, main page]
Scribd Logo
Upload

Welcome to Scribd!

  • 42 views

    Esc201: Introducton To Electronics: Sinusoidal Steady State Analysis

    Uploaded by

    ash jay
    The document is about sinusoidal steady state analysis in electrical circuits. It discusses canonical forms for sinusoidal waveforms, average power calculations, phasor representations, complex impedances of circuit elements like resistors, inductors and capacitors. It provides examples of calculating currents and voltages in RLC circuits using phasor analysis and applying concepts like superposition theorem. Finally, it discusses power calculations and shows that while the average power dissipated in an inductor or capacitor is zero, power supplied by the source is dissipated in the resistances in the circuit.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    Esc201: Introducton To Electronics: Sinusoidal Steady State Analysis

    Uploaded by

    ash jay
    42 views35 pages
    The document is about sinusoidal steady state analysis in electrical circuits. It discusses canonical forms for sinusoidal waveforms, average power calculations, phasor representations, complex impedances of circuit elements like resistors, inductors and capacitors. It provides examples of calculating currents and voltages in RLC circuits using phasor analysis and applying concepts like superposition theorem. Finally, it discusses power calculations and shows that while the average power dissipated in an inductor or capacitor is zero, power supplied by the source is dissipated in the resistances in the circuit.

    Original Description:

    esc 201 iitk lec10

    Original Title

    L10

    Copyright

    © © All Rights Reserved

    Available Formats

    PDF, TXT or read online from Scribd

    Did you find this document useful?

    Is this content inappropriate?

    The document is about sinusoidal steady state analysis in electrical circuits. It discusses canonical forms for sinusoidal waveforms, average power calculations, phasor representations, complex impedances of circuit elements like resistors, inductors and capacitors. It provides examples of calculating currents and voltages in RLC circuits using phasor analysis and applying concepts like superposition theorem. Finally, it discusses power calculations and shows that while the average power dissipated in an inductor or capacitor is zero, power supplied by the source is dissipated in the resistances in the circuit.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    42 views35 pages

    Esc201: Introducton To Electronics: Sinusoidal Steady State Analysis

    Uploaded by

    ash jay
    The document is about sinusoidal steady state analysis in electrical circuits. It discusses canonical forms for sinusoidal waveforms, average power calculations, phasor representations, complex impedances of circuit elements like resistors, inductors and capacitors. It provides examples of calculating currents and voltages in RLC circuits using phasor analysis and applying concepts like superposition theorem. Finally, it discusses power calculations and shows that while the average power dissipated in an inductor or capacitor is zero, power supplied by the source is dissipated in the resistances in the circuit.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 35

    ESc201 : Introducton to Electronics

    Sinusoidal Steady state Analysis

    Dept. of Electrical Engineering


    IIT Kanpur

    1
    Recap
    Canonical Form x(t )  xm cos(t   )
    Phase difference is usually considered between -180 to 180o

    2
    Average Power Vrms
    Vrms 
    Vm Vm2
    pavg  pavg 
    R 2 2R
    Im 1 2
    I rms  pavg  Im R
    2 2

    Phasor
    v(t )  Vm cos(t   ) Vm 
    2
    Recap Complex Impedances
    Inductor

    VL  I L  Z L Z L  j L

    3
    Resistor R

    v(t)

    v(t )  VM cos(t   ) i (t )  VM cos(t   )


    R
    VM
    VR  VM  IR  
    R
    VR
    IR 
    R
    4
    Example-5 i(t) L=0.1H R=50

    v(t)

    v(t )  2 cos(200t  45) V   200 rad/s

    j20 50

    Z L  j L

    VS  245 V 5
    Example-5 contd.
    50+j20
    Zeq

    VS  245 V

    245 245
    I    0.03723.2 A
    50  j 20 53.8521.8

    i (t )  0.037 cos(200t  23.2) A

    6
    j20 50

    VS  245 V

    50
    VR  2 45  V
    50  j 20

    Concept of voltage or current division can be used as before

    7
    Capacitor
    v(t )  VM cos(t   )

    dvc
    ic  C
    dt

    i(t )   CVM sin(t   )


    i(t )  CVM cos(t    90 ) o

    VC  VM  I C  CVM   90
    In a capacitor, current leads voltage by 900 8
    Capacitor
    VC  VM 

    I C  CVM   90

    I C  C90 VM 

    I C  jCVC

    1 1
    VC  I C  ZC ZC  j
    jC C

    9
    10
    Example-6

    11

    12
    A

    13
    V

    VS  10030

    I  0.707  15

    14
    Example-7

    15
    V

     V

    16
    Currents Z RC  50  j 50 

    A
    A
    17
    Example-8

    18
    19
    Example-9

    20
    21
    Example-10

    22
    23
    25
    Superposition Theorem is also applicable for independent
    sinusoidal sources
    26
    27
    Example-11

    28
    29
    Power dissipation in RLC Circuits
    For Resistance T
    v (t ) 2 1 v(t ) 2
    0 R dt
    R
    p pavg 
    R T
    v(t) 2
    Vrms
    pavg 
    R
    Vm
    Vrms 
    2

    pavg  I rms
    2
    R
    Im
    I rms 
    2 30
    L

    v(t)

    pavg  0
    31
    C

    v(t)

    pavg  0

    32
    General Rule v(t )  VmCos(t )
    i(t )  I mCos(t   )

    T
    1
    p
    T  v(t )  i(t )dt
    0

    For a resistor PF = 1, while for inductor and capacitor it is 0


    1 1
    j L   L 90 ;  j    90
    C C
     is phase difference between voltage and current 33
    Find the average power drawn from the supply

    0.1
    I Rrms   0.071
    Where is this power dissipated? 2

    P  VRrms  I Rrms cos   I 2


    Rrms  R  0.5W 34
    Average power dissipated through the inductor
    VL  j100  I 14.14  45
        45  135  90
    P 0
    1
    PI  R  0.5W P  I Rrms R 
    2 2 2
    Rrms
    IR R
    2 35
    Should a Power company charge a person even though power
    consumed is zero?

    L Power
    v(t)
    Meter

    pavg  0
    Rwire

    L Power
    v(t)
    Meter
    Power is dissipated and
    somebody has to pay for it.
    Rwire 36

    You might also like