Overview
This lecture introduces Kirchhoff's two circuit laws—Loop Rule and Junction Rule—and explains how to apply them to solve for currents and voltages in series and parallel circuits.
Kirchhoff’s Circuit Laws
- Kirchhoff's laws help analyze potential difference (voltage) and current in electrical circuits.
- The two main laws are the Loop Rule (KCL) and the Junction Rule (KVL).
Loop Rule (Kirchhoff's Voltage Law)
- The total potential difference around any closed loop in a circuit is zero.
- In a loop, sum all voltages: 0 = total battery voltage - voltage drops across all resistors.
- When tracing a battery from negative to positive, add its voltage; subtract voltage drops across resistors when moving with current.
- For a series circuit: V_total = V1 + V2 + V3.
- Voltage across a resistor: V = I × R, so V1 = I × R1, etc.
Junction Rule (Kirchhoff's Current Law)
- At any junction (point where wires meet), total current entering equals total current leaving.
- For example, in a split after R1: I_in = I2 + I3.
Applying the Laws to Circuits
- In circuits with multiple loops, define separate loops and apply Loop Rule to each.
- For parallel circuits, Junction Rule is crucial because current splits at junctions.
- Set up equations for each loop (using Loop Rule) and junction (using Junction Rule).
- Substitute Ohm's Law (V = IR) into equations as needed to solve for unknowns.
- Complex circuits may require solving a system of equations for unknown currents or voltages.
Key Terms & Definitions
- Loop Rule (Kirchhoff's Voltage Law) — The sum of potential differences around any closed loop is zero.
- Junction Rule (Kirchhoff's Current Law) — The total current entering a junction equals the total current leaving.
- Closed Loop — Any path in a circuit that forms a complete circle.
- Junction — A point where three or more conductors meet.
- Ohm's Law — Voltage across a resistor equals current times resistance (V = IR).
Action Items / Next Steps
- Practice setting up and solving circuit problems using Loop Rule and Junction Rule.
- Prepare for algebraic manipulation of equations in multi-loop or parallel circuits.