Lecture Notes: Kirchhoff's Voltage Law

Introduction

• Focus: Kirchhoff's Voltage Law (KVL)
• Importance: Essential for analyzing electrical circuits
• Two Kirchhoff's Laws:
  • Voltage Law (covered in this lesson)
  • Current Law (to be covered in next lesson)

Determining Current Direction

• Basic Rule: Current flows from the (+) pole to the (–) pole of the source
• Approach:
  • Estimate direction if unclear
  • Positive current value = correct direction
  • Negative current value = opposite direction

Kirchhoff's Voltage Law

• Concept: The sum of voltages around a loop equals zero
• Formula:
  • Produced and Consumed Voltage: ( VT = V1 + V2 + V3 )
  • Rearranged: ( -VT + V1 + V2 + V3 = 0 )

Practical Example

• Objective: Find voltage across resistors and circuit current
• Steps:
  1. Determine current direction
  2. Assign voltage expressions: ( V1 = I \cdot R1, V2 = I \cdot R2, V3 = I \cdot R3 )
  3. Calculate main current: ( I = 45V / 22.5k\Omega = 2mA )
  4. Voltage calculations:
     • ( V1 = 10V )
     • ( V2 = 20V )
     • ( V3 = 15V )
• Observation:
  • Total consumed voltage = produced voltage
  • Voltage proportional to resistance values

Complex Circuits with Multiple Voltage Sources

• Example Setup:
  • Two sources: VA and VB
  • Assume current direction (e.g., clockwise)
• Voltage Law Application:
  • ( -VA + V1 + VB + V2 = 0 )
• Calculations:
  • Current: ( -20V / 5k\Omega = -4mA ) (direction is counterclockwise)
  • Recalculate voltages:
    • ( V1 = 8V )
    • ( V2 = 12V )
• Verification:
  • Generated voltage ( = VB - VA = 20V )
  • Consumed voltage ( = 20V )

Application in Various Circuit Components

• General Application: Applies beyond resistors (e.g., with diodes, transistors)
• Examples:
  • Circuit with diode and resistor: ( -V + VD + VR = 0 )
  • BJT transistor circuit:
    • First mesh: ( -4V + IB \cdot 20k\Omega + VBE = 0 )
    • Second mesh: ( -6V + IC \cdot 100k\Omega + VCE = 0 )

Conclusion

• Summary: KVL ensures sum of voltages in circuit loops equals zero
• Next Steps: Upcoming lesson on Kirchhoff's Current Law
• Closing: Hopeful for constructive learning in future sessions