Overview
This lecture explains Kirchhoff's Junction Rule (Current Rule) and Loop Rule (Voltage Rule), their application in analyzing complex circuits, and how to set up the corresponding equations.
Kirchhoff's Laws
- Junction Rule: The sum of currents entering a junction equals the sum leaving it.
- Loop Rule: The sum of potential differences around any closed circuit loop is zero.
- Junction Rule is also called the Current Rule; Loop Rule is also called the Voltage Rule.
Key Circuit Definitions
- Junction: A point where two or more wires meet in a circuit.
- Branch: A path connecting two junctions.
- The number of branches equals the number of separate currents in the circuit.
Setting Up Circuit Analysis
- Assign a current to each branch (e.g., i₁, i₂, i₃) and choose their directions arbitrarily.
- Use the Junction Rule at any junction to create one equation relating the currents.
- Only one Junction Rule equation is needed if others are redundant.
Applying the Loop Rule
- Identify independent loops; for a circuit with three branches, you typically need two Loop Rule equations and one Junction Rule equation.
- Choose a direction (clockwise or counterclockwise) for each loop and mark it on the diagram.
- For batteries: Crossing from negative to positive terminal is a positive voltage (+), positive to negative is negative (−).
- For resistors: Going through a resistor in the current’s direction is negative voltage (−IR); opposite direction is positive (+IR).
Example Equation Setup
- Use V = IR to convert voltage terms to current terms for resistors.
- Combine like terms to simplify equations.
- Example: 24 − 6i₁ + 3i₂ = 0 for a given loop.
Key Terms & Definitions
- Junction — Point where two or more conductors meet.
- Branch — Section of a circuit between two junctions.
- Kirchhoff's Junction Rule — Current into a junction equals current out.
- Kirchhoff's Loop Rule — Total voltage change around a loop is zero.
- V = IR — Ohm’s Law: voltage equals current times resistance.
Action Items / Next Steps
- Practice identifying branches, junctions, and assigning currents in different circuits.
- Write out Junction Rule and Loop Rule equations for sample circuits.
- Solve systems of equations to find unknown currents.