Kirchhoff's Laws

While Ohm's Law works perfectly for simple circuits, real-world circuits often have multiple components, branches, and loops. Kirchhoff's Laws, formulated by German physicist Gustav Kirchhoff in 1845, extend our analysis capabilities to handle any circuit, no matter how complex. Combined with Ohm's Law, these two principles let you solve for any unknown in any circuit.

Objectives

• Understand and apply Kirchhoff's Current Law (KCL)
• Understand and apply Kirchhoff's Voltage Law (KVL)
• Identify nodes, branches, and loops in circuits
• Analyze series and parallel resistor circuits
• Solve multi-loop circuits systematically
• Know when to use KCL vs KVL vs both

Key Takeaways

• KCL: Current in = Current out at any node (conservation of charge)
• KVL: Voltages around a loop sum to zero (conservation of energy)
• Series: same current, voltages add, resistances add
• Parallel: same voltage, currents add, 1/R_eq = 1/R1 + 1/R2
• For multi-loop circuits, use both KCL and KVL
• Combined with Ohm's Law, you can solve any circuit

Practice Problems

Problem 1: Three currents meet at a node: I1 = 3A and I2 = 2A enter, I3 leaves. What is I3?

Problem 2: A 9V battery powers two series resistors. If V1 = 3V, what is V2?

Problem 3: R1 = 100Ω, R2 = 200Ω, R3 = 200Ω in series with 15V. Find the current.

Problem 4: A 24V source powers R1 = 120Ω and R2 = 80Ω in parallel. What is the total current?

Problem 5: At a node: I1 = 10A enters, I2 = 4A leaves, I3 = 2A leaves. What is I4?