12. RC Circuits

• VR I lead source Vs
• Vc lags Vs
• Phase angle between VR I and Vc always 90º

  
• Signal Generators


  • Function sine square
  • pulse regular triangular (ramp)
• series RC circuit


  • Resistive
  • Capacitive
• Impedance


  Total opposition to sinusoidal current (Ohms)

  
• Phase angle


  Phase difference between the total current and the source voltage

  
• Vc lags I by 90º
• VR in phase with I
• Polar form


  • Phase angle
  • Ohms
• Analysis of series RC circuits

  1. Determine source voltage

  2. Draw phasor diagram

  
• Phasor quantities


  Z, V, I
• Ohms's Law = Kirchhoffs Voltage Law
• Phasor Algebra: multiplication and division are easiest in polar form
• Applying Ohm's Law


  1. V=IZ = (0.2Ð0°mA) (18.8Ð-57.8°)kW

  2. VS = 3.76V

  3. I = 0.2 mA
• Current and Voltage Relationships in a Series RC Circuit

  • Current same in R and C
  • Kirchhoff's Voltage Law: Vs = VR + VC
  • Vc lags VR by 90°
  • Vs = VR - jVc

  
• Conductance, Susceptance and Admittance

  • Capative susceptance
  • Admittance (Y)
  • Siemens (S)
• Total Admittance Y = G + BC = 3.03 mS + j 1.26 mS
• Applying Ohms Law


  1. IT = VS Y = (10 Ð0V)(492 Ð22.5°µS)

  2. IT = 4.92 Ð22.5° mA
• Analysis of Parallel RC Circuits

  • Ohms Law and Kirchhoff's Current Law
  • For convenience in parallel circuits
• Relationships of the Currents and Voltages in Parallel RC Circuits

  • Current divides
  • VS appears across resistive and capacitive branches
  • Vc leads voltage by 90°
  • IR VR Vc in phase with voltage VS

  
• Series – Parallel RC Circuits


  Total Impedance, Total current, phase angle by which IT leads VS

  
• Power in RC Circuits

  • Purely resistive: power dissipated as heat
  • Purely Capacitive: storage and released, no net energy loss
  • Some stored, some lost as heat
• True power


  Ptrue=I2R (Watt)
• Reactive power


  Pr = I2 XC VAR
• Applications: Phase Shift


  • RC lag network
  • Output lags input
  • CRO display
  • Phase difference between Input and Output
• Magnitude of the Output Voltage

  Imagine R,C lag network as a voltage divider

  
• RC lead network


  • Current leads I/p voltage
  • Vout taken across resistor
• Magnitude of the Output Voltage


  Voltage Divider
• RC Circuit as a filter

  • Low pass filter
  • High Pass filter
• Troubleshooting


  Effects of a leaky capacitor
• Phase shift