Kirchhoff's laws are two fundamental principles used in circuits involving electric currents and voltages, formulated by German physicist Gustav Kirchhoff in 1845. These laws describe how electric current and voltage behave in electrical circuits and are the basis for analyzing complex circuits. There are two Kirchhoff's laws: Kirchhoff's Current Law (First Law) and Kirchhoff's Voltage Law (Second Law).
Kirchhoff's Current Law (also known as the Law of Conservation of Charge) states that the algebraic sum of currents entering any node (connection point) in an electrical circuit is zero. This means that the total current entering a node is equal to the total current leaving the node.
Mathematical expression:
∑ I in = ∑ I out
or
∑ I = 0
Significance: This law is based on the conservation of electric charge. No electric charge can accumulate at any node in a circuit—the charge entering the node must leave it.
Example: If three currents (I1, I2, I3) enter a node, and two currents (I4, I5) leave the node, the following applies:
I1 + I2 + I3 = I4 + I5
Kirchhoff's Voltage Law (also known as the Law of Conservation of Energy) states that the algebraic sum of all voltages around a closed loop in an electrical circuit is zero. In other words, the sum of all voltage rises and drops in any closed loop is zero.
Mathematical expression:
∑ V = 0
Significance: This law is based on the principle of energy conservation. The electrical energy supplied by voltage sources (batteries, generators) in the circuit must equal the sum of the voltages consumed by the loads (resistors, inductors, capacitors) in the circuit.
Example: In a simple circuit containing a voltage source (Vbattery) and two resistors with voltages V1 and V2, the following applies:
Vbattery - V1 - V2 = 0
or
Vbattery = V1 + V2
Kirchhoff's laws are key tools for understanding and analyzing electrical circuits. They allow engineers and technicians to accurately calculate currents and voltages in different parts of circuits and ensure that systems operate efficiently and safely. Although they have certain limitations, their practical value in electrical engineering and electronics is invaluable.
