Lecture on Kirchhoff's Voltage Law (KVL)

Introduction to Kirchhoff's Voltage Law

• Kirchhoff's Voltage Law (KVL) states that the sum of the voltages around any closed circuit must equal zero.
• Voltage contributions in a circuit can be either positive or negative.
  • Positive Voltage: Occurs when energy is added to the charges.
  • Negative Voltage: Occurs when energy is consumed from the charges.

Voltages in Circuit Components

Resistors

• Current flows from high potential to low potential.
• Resistors consume energy, causing a voltage drop (negative voltage).
• Voltage Drop Formula: ( V = - I \times R )

Batteries

• Batteries can increase or decrease energy depending on the direction of current related to the polarity:
  • Increase Energy (Positive Voltage): Current flows from low potential to high potential.
  • Decrease Energy (Negative Voltage): Current flows from high potential to low potential.

Analyzing Circuit Examples

Basic Circuit with a Battery and Resistors

1. Circuit Components:

   • One battery (positive terminal to negative flow direction)
   • Three resistors (R1, R2, R3)
   • Battery voltage: 12V; Resistor values: 8Ω, 10Ω, 12Ω

2. Applying KVL:

   • The sum of the voltages (battery and resistors) is zero.
   • Equation: ( 12 - (8 \times I) - (10 \times I) - (12 \times I) = 0 )
   • Solve for current: ( I = 0.4 \text{ A} )

3. Calculating Electric Potential:

   • Potential at a point is calculated based on voltage drops.
   • Example calculated potentials:
     • Point A: 12V
     • Point B: 8.8V
     • Point C: 4.8V

Circuit with Two Batteries

1. Circuit Components:

   • Two batteries (12V and 8V)
   • Two resistors (50Ω and 30Ω)

2. Direction of Current:

   • Both batteries support a clockwise current flow.

3. Applying KVL:

   • Equation: ( 12 - (50 \times I) + 8 - (30 \times I) = 0 )
   • Solve for current: ( I = 0.25 \text{ A} )

4. Calculating Electric Potential:

   • Voltage potential at various points calculated using voltage drops across resistors and batteries.

Complex Circuit with Multiple Batteries and Resistors

1. Circuit Components:

   • Three batteries (50V, 10V, 20V)
   • Two resistors (30Ω and 70Ω)

2. Direction of Current:

   • Determined by the strongest battery (50V) overpowering the other two combined.

3. Applying KVL:

   • Equation: ( 50 - (30 \times I) - 20 - 10 - (70 \times I) = 0 )
   • Solve for current: ( I = 0.2 \text{ A} )

4. Calculating Electric Potential:

   • Use voltage drop calculations for each component.

Conclusion

• Resistors always decrease energy and thus have negative voltage (voltage drop).
• Batteries can either increase or decrease energy based on current direction relative to their polarity.
• Understanding these concepts is crucial for analyzing more complex circuits effectively.