Upon successful completion of this module, the student will be able to:
State Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL).
Identify nodes, branches, and loops in a complex DC circuit.
Apply KVL and KCL to set up a system of equations for circuits that cannot be solved by simple series-parallel rules.
Solve for unknown currents and voltages in multi-source circuits.
Apply Kirchhoff's Laws as a foundational tool for advanced troubleshooting.
So far, we’ve tackled series, parallel, and combination circuits. We have a solid toolkit. But what happens when you encounter a circuit so complex it can't be simplified? A circuit with multiple power sources fighting each other, or with interconnected loops that defy basic series-parallel rules?
This is where you need to bring out the heavy artillery: Kirchhoff's Laws.
These two laws are the universal, unbreakable rules of circuit analysis. They work on any DC circuit, no matter how complicated. Mastering Kirchhoff's Laws is the final step in becoming a true diagnostic technician, allowing you to mathematically prove what’s happening inside the most complex systems, from a vehicle's charging system to an industrial power backup unit.
These laws are elegantly simple in concept.
1. Kirchhoff's Current Law (KCL): The Law of Junctions
The Law: The sum of all currents entering a node (a junction point) must equal the sum of all currents leaving that node.
The Simple Analogy: Think of a 'T' fitting in a plumbing system. If you have 5 gallons per minute flowing in, you can't have 3 gallons coming out of one pipe and 3 gallons out of the other. It has to add up. What goes in, must come out.
The Industrial Example: A terminal block in a control cabinet. A single large wire brings 5A of current to the block. That block feeds three separate circuits: a PLC (2A), an HMI screen (1.5A), and a sensor bank (1.5A). The current splits, but the total leaving (2 + 1.5 + 1.5 = 5A) is exactly what came in.
2. Kirchhoff's Voltage Law (KVL): The Law of Loops
The Law: The sum of all voltage rises (from sources like batteries) and voltage drops (across components like resistors) in any closed loop must equal zero.
The Simple Analogy: Think of a roller coaster ride. As you get pulled up the main hill, you gain a specific amount of height (a voltage rise). As you go through all the twists, turns, and loops, you use up exactly that amount of height. When you return to the station, you are back at your starting height. The gains and losses in any full lap must cancel out to zero.
The Automotive Example: A car's charging system. The alternator provides a voltage rise of +14.4V. As that energy flows through the circuit, it drops across the wiring, the lights, and even the battery as it charges. If you could measure every single drop in that loop, they would add up to exactly -14.4V, making the total sum zero.
This is the systematic procedure for analyzing a complex circuit. It looks intimidating, but it's a step-by-step process.
The Scenario: A circuit has two power sources (a 12V battery and a 9V backup) and three resistors that aren't in a simple series-parallel layout.
Assign Currents: Label the current in each branch of the circuit (e.g., I₁, I₂, I₃). Your initial guess for the direction doesn't matter! If you guess wrong, the math will give you a negative answer later, telling you it flows the other way.
Mark Polarity: For each resistor, mark the side where your assumed current enters with a '+' and the side where it leaves with a '-'. This represents the voltage drop.
Write KCL Equation: Pick a major junction (node) and apply KCL. Example: I₁ = I₂ + I₃.
Write KVL Equations: Trace each loop in the circuit, writing a KVL equation for each. Start at one point, add your voltage rises and subtract your voltage drops, and finish back where you started, setting it all equal to zero.
Solve the System: You now have a set of simultaneous equations. Solve them using algebra (substitution) to find the true value and direction for every current.
This is where the theory becomes a powerful diagnostic tool.
The System: A critical control panel has a main 24V power supply. For backup, a 24V battery is also connected to the system. The system powers two loads: a "Critical Load" (a PLC that must never lose power) and a "Non-Critical Load" (cabinet lighting).
The Analysis:
Normal Operation: Using Kirchhoff's Laws, you can write the equations for this multi-source circuit. The math would prove that the main 24V supply (which might actually be 24.5V) provides all the current for both the PLC and the lights. It also provides a small "trickle charge" current to the battery (which might be resting at 24.1V).
Power Failure: Now, the main 24V supply goes dead (becomes 0V). The equations instantly change. KVL now shows that the backup battery is the only voltage source in the loop. It becomes the source, providing a current that flows out of the battery to keep the Critical Load (the PLC) running. The Non-Critical Load (the lights) goes dark because of how the circuit is designed.
By applying Kirchhoff's Laws, you can analyze and predict exactly how the currents will flow in both normal and failure conditions.
You are a top-tier auto technician diagnosing a "parasitic draw"—something is draining the battery overnight. The draw is very small, making it hard to find.
Your Diagnostic Plan:
Hypothesis: There is a small, unwanted voltage drop happening somewhere in the car, indicating a path to ground that shouldn't exist.
The KVL Application (Voltage Drop Testing): KVL states that the voltage drops in a loop must sum to zero. A perfect wire or a good switch should have a voltage drop of 0V. Any reading other than zero indicates a problem.
Create a Test Plan:
Set up your multimeter to read millivolts (mV).
Go to the fuse box. Instead of pulling fuses (which can reset modules), you will measure the voltage across every fuse with the car turned off.
You measure across the radio fuse: 0mV. Good. You measure across the headlight fuse: 0mV. Good.
You measure across the interior light module fuse: 9mV. This is your culprit!
The Conclusion: That tiny 9mV drop, which should be 0mV, proves that a small current is flowing through that fuse's circuit even when the car is off. You have just used Kirchhoff's Voltage Law to create a non-invasive test plan and successfully pinpointed the faulty circuit without taking anything apart.
(Remembering)
Kirchhoff's Current Law (KCL) deals with the currents at a circuit ______, while Kirchhoff's Voltage Law (KVL) deals with the voltages in a closed ______.
What is the expected sum of all voltage rises and drops in any complete, closed loop of a circuit?
(Understanding)
3. Using the roller coaster analogy, explain why KVL works. What do the "voltage rises" and "voltage drops" represent in the analogy?
4. A student assumes a current direction while setting up a Kirchhoff's analysis. After solving the equations, they get a negative answer for that current (e.g., -0.5A). What does this negative sign signify?
(Applying)
5. Three wires meet at a single node. Current I₁ (2A) and I₂ (3A) are flowing into the node. What is the value and direction of the current in the third wire, I₃?
6. In a simple series circuit with a 12V battery and two resistors, R1 drops 7V. What is the voltage drop across R2?
(Analyzing)
7. A technician measures the voltage across a car's battery terminals as 12.6V. They then measure the voltage directly at the headlight bulb's terminals as 11.9V. Analyze this situation using KVL and determine the voltage drop in the wiring between the battery and the headlight.
8. A circuit has two 12V batteries and a single resistor connected in a loop. However, the batteries are connected "fighting" each other (positive to positive). Analyze this loop using KVL and determine the voltage across the resistor.
(Evaluating)
9. A technician is analyzing a complex circuit diagram. They identify three independent loops and two principal nodes. They decide to write three KVL equations and two KCL equations to solve the circuit. Evaluate this approach. Is it the most efficient way to set up the system of equations, or is there a redundancy?
(Creating)
10. A boat has two batteries (Main and Auxiliary) that can be connected via a switch. The engine will not crank. You suspect a bad connection on a battery cable is preventing the high current from flowing. Create a troubleshooting step using Kirchhoff's Voltage Law (as a voltage drop test) to prove if a battery cable connection is faulty while a helper attempts to crank the engine.
Various circuits using basic electrical kits, mobile modular, control circuit panels