Electrical circuits are governed by fundamental conservation laws. The two most important principles are Kirchhoff's Current Law, which deals with current conservation at nodes, and Kirchhoff's Voltage Law, which deals with energy conservation around closed loops. These laws provide the mathematical foundation for analyzing any electrical circuit, from simple resistor networks to complex electronic systems.
Kirchhoff's Current Law states that the algebraic sum of all currents at any node in a circuit must equal zero. This fundamental principle is based on charge conservation - electrical charge cannot accumulate at a node. In our sign convention, currents entering a node are considered positive, while currents leaving are negative. For this node example, we have currents I1 and I2 entering, and I3 and I4 leaving, giving us the equation: I1 plus I2 minus I3 minus I4 equals zero.
Let's solve a practical KCL problem. We have a node with four currents: I1 equals 3 amperes entering, I2 equals 2 amperes entering, I3 equals 1 ampere leaving, and I4 is unknown leaving. Using KCL, we write: I1 plus I2 minus I3 minus I4 equals zero. Substituting the known values: 3 plus 2 minus 1 minus I4 equals zero. Simplifying: 4 minus I4 equals zero. Therefore, I4 equals 4 amperes leaving the node.
Kirchhoff's Voltage Law states that the algebraic sum of all voltages around any closed loop in a circuit must equal zero. This fundamental principle is based on energy conservation - electrical energy cannot be created or destroyed within a loop. When traversing a loop, voltage sources represent energy rises and are positive, while resistors represent energy drops and are negative. In this example loop, we have a 12-volt source providing energy, and three resistors dropping 4, 3, and 5 volts respectively, giving us: plus 12 minus 4 minus 3 minus 5 equals zero.
Let's solve a practical KVL problem. We have a circuit loop with a 15-volt source and three resistors. R1 drops 4 volts, R2 drops 6 volts, and we need to find the voltage drop across R3. Using KVL, we write: voltage source minus V1 minus V2 minus V3 equals zero. Substituting known values: 15 minus 4 minus 6 minus V3 equals zero. Simplifying: 5 minus V3 equals zero. Therefore, V3 equals 5 volts. We can verify: 15 minus 4 minus 6 minus 5 equals zero, confirming our answer.