13. RL Circuits

• Topics


  • Voltage and Current Relationship
  • Impedance and Phase Angle
  • Series RL
  • Parallel RL
  • Series – Parallel RL
  • Power in RL
  • Applications
  • Troubleshooting
  • Sinusoidal Response of RL Circuits

  
• Sinusoidal Response of RL Circuits


  • Opposite of RC Circuits
  • Vs Sinusoidal ® VR, VL, I sinusoidal
  • Same frequency ® phase shift due to inductor
  • Different amplitudes
  • Depend on resistance and inductive reactance
• Phasor


  XL = jXL
• Impedance Triangle


  • R, XL are phasors
  • Length of vector represents magnitude of the quantity
  • Phase angle between the applied voltage and the current in an RL Circuit

  
• Inductive Reactance


  XL = jwL = j2pfL
• Ohm's Law
• Phase angle θ between VR and VS is 32.1°
• Current and Voltage Relationships in Series RL

  1. VS=VR+ jVL

  2. Phasors

  3. Kirchhoff

  4. Magnitude of VS ((VS))

  5. Phase angle θ between VR and VS

  
• As frequency (f) increases

  XL increases, Z increases and θ increases
• Impedance and Phase Angle of Parallel RL Circuits

  • Magnitude of Z
  • Phase angle between applied VS and I
  • Conductance, susceptance (inductive) and admittance

  
• Conductance = I/R
• Inductive susceptance = BL
• Admittance = 3.42mS at -27.7°
• Currents and Voltages in Parallel RL Circuits

  1. VS appears across R, L, Þ VS VR VL in phase and equal magnitude

  2. IR in phase with VR

  3. IL lags VL (and IR) by 90°

  4. IT =IR -jIL

  
• Magnitude of IT is 96.8mA
• Phase angle between resistor current and total current is -55.7°

  
• IL=80mA, IR=54.5mA
• Series – Parallel RL Circuits


  1. Series:

  2. Parallel:
• Voltage across each element in polar form
• Voltage across each element in rectangular form
• Power in RL Circuits

  • heat
  • Stored and returned
  • In B field
  • No net energy loss
  • Power factor = cosθ

  
• Current magnitude
• True Power
• Reactive Power
• Apparent Power
• Significance of the Power Factor

  • How much useful power is transferred to load
  • Effect of power factor on system requirements such as a source rating, VA and conductor size

  
• Ideally PF»1 – source transfers most power to load as useful or true power
• Power Factor Correction


  • Increase power factor of inductive load by adding capacitor in parallel
  • RL lead network
  • Phase shift
  • Inductor voltage (VL) is the output
  • Vout leads input

  
• 1. L lag network


  • Output across resistor
  • Magnitude of Output Voltage
  • Phase Lead RL network
  • Visualise RL network as a voltage divider: output across XL
  • Phase lag RL network
  • Voltage divider : output across R
• Low Pass Filter


  Output voltage as a function of frequency
• High Pass Filter


  • Response Curve for a low pass filter
  • Response Curve for a high pass filter