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Time to read 6 min
Introduction
In electrical circuit analysis, two of the most fundamental rules are Kirchhoff’s Current Law (KCL) and Kirchhoff’s Voltage Law (KVL). These laws describe the flow of current through junctions and the distribution of voltage in closed loops, forming the backbone of almost all circuit problem-solving methods.
This article introduces the basics of KCL and KVL, and shows how to understand them through practical measurements on a breadboard. The content is adapted from Experiment 05 in our Basic Electrical Circuits book, where theory meets hands-on verification. If you’re interested in building these experiments yourself, try this kit and ieally buy with Lab-On-The-Go.
Kirchhoff’s Current Law (KCL) describes the relationship between currents meeting at a single point, known as a node. It states that the sum of currents flowing into a node is always equal to the sum of currents flowing out of that node. In other words, electric charge is conserved at every connection point in a circuit: no current is lost or mysteriously created.
Mathematically, the KCL equation is written as:
This means the four branch currents at the node on the right hand side has:
I2 + I3 = 11 + I4
Sometimes you will also see it written in an algebraic sum form: I1+(−I2)+I3+(−I4)=0
In this version, the current direction is represented by signs. If all currents entering the node are defined as positive, then all currents leaving the node will be negative. This choice of sign is completely relative as long as you remain consistent throughout the analysis.
We can verify KCL using a simple breadboard experiment. Build the circuit as shown and focus on node b, where three branch currents I1, I2, and I3 meet. Note that before solving the circuit, we do not know the true directions of these currents, so we simply assume them arbitrarily, as indicated in the diagram. It is important to note that the assumed currents may match the actual directions or be opposite to them.
Therefore, according to the directions of the assumed currents in the diagram, we have the following KCL equation:
I1 + (-I2) + I3 = 0
or if you prefer, can be also written as:
I1 + I3 = I2
On breadboard, we use a digital multimeter to measure the series current of each branch. Note that the polarity of the meter should be consistent with the directions of your assumption currents. If the reading shows a positive value, say 8mA, it means the actual current is same with your assumption current; if the reading shows a negativ value, say -5mA, it means the actual current has 5mA magnitude but in the opposite direction of your assumption current.
Once all three readings are taken, you can substitute them into the KCL equation (I1+I3=I2) to check if the law holds. Small deviations from zero are normal due to measurement tolerances and component inaccuracies, but the results should be close enough to confirm KCL in practice.
Kirchhoff’s Voltage Law describes how voltages behave in a closed loop within an electrical circuit. It states that the algebraic sum of all voltage rises and drops around any closed loop is always zero. This is a direct consequence of the conservation of energy—whatever electrical energy is supplied by sources in the loop must be exactly balanced by the energy consumed by the loads.
Mathematically, KVL can be written as:
or simply:
As with KCL, the initial assumption is arbitrary, and should be consistent throughout the analysis.
The sign of each voltage depends on the chosen loop direction and the polarity across each component. Similarly, to solve the circuit, we can still assign voltage polarities arbitrarily and then apply the KVL equation based on that assumption. If the actual voltage polarity is opposite to your assumed loop direction, the measured value will appear as a negative number, indicating the true polarity is reversed.
In this setup, we verify KVL by measuring voltages around loop a. The assumed loop direction is counterclockwise, starting from the positive terminal of the source VS, passing through R1 and R2, and returning to the source. For measurements, the meter's polarity should match to the polarity of your assumed voltages.
According to KVL, the sum of the source voltage and the signed voltage drops should be zero:
After recording the measured values, substitute them into the equation. If the total is close to zero within reasonable measurement error, KVL is confirmed.
Kirchhoff’s Current Law (KCL) and Kirchhoff’s Voltage Law (KVL) are more than just mathematical tools, they are direct consequences of two fundamental conservation principles in physics.
While KCL and KVL provide the theoretical backbone for circuit analysis, they also serve as stepping stones to more systematic methods. By combining these laws with Ohm’s Law, engineers often use nodal analysis (based on KCL) to find unknown node voltages and mesh analysis (based on KVL) to find loop currents efficiently.
A node is any point where two or more circuit elements connect , and understanding node behavior is the starting point for applying both KCL and nodal analysis effectively.
KCL ensures current balance at every node by enforcing the conservation of electric charge—currents entering a node equal currents leaving it.
KVL ensures energy balance in every loop by stating that the algebraic sum of all voltage rises and drops in a closed loop is zero.
Sign conventions matter: assume directions or polarities consistently, and let measurement signs indicate whether your initial assumption was correct.
KCL deals with current flow at a node and ensures that the total current entering equals the total current leaving. KVL applies to a closed loop and ensures that the sum of all voltage rises and drops is zero.
They are fundamental tools for circuit analysis and form the basis of advanced techniques such as nodal analysis and mesh analysis , allowing engineers to solve for unknown voltages and currents in complex electrical networks.
Yes. These laws are valid for both direct current (DC) circuits and alternating current (AC) circuits , as they are derived from universal conservation principles.
You can choose directions arbitrarily at the start. If the calculated result is negative, it simply means the actual direction is opposite to your initial assumption.
KCL is the backbone of nodal analysis , where you solve for node voltages. KVL is the basis for mesh analysis , where you solve for loop currents. Both methods make large circuit problems more manageable.
Daniel Cao
Daniel Cao is the founder of EIM Technology, where he creates hands-on, beginner-friendly electronics education kits that blend practical hardware with clear, structured learning. With a background in engineering and a passion for teaching, he focuses on making complex concepts accessible to learners from all disciplines.
