Difference Between Ohm’s Law and Kirchhoff’s Law

Mathematical expressions are very helpful when it comes to describing electrical circuits. With the help of a set of equations, it becomes very easy to solve and calculate current and voltages in a circuit. There are two laws that help in determining the circuit equations and they are Ohm’s law and Kirchhoff’s law. 

The relationship between Ohm’s law and Kirchhoff’s law is that the former law is used for explaining the basic principles while the latter is used for explaining the features of an electric circuit, while the theory explains the variables of the circuit. So, what is the key difference between Ohm’s law and Kirchhoff’s law?

The key difference between the two is that Ohm’s law is used for explaining the relation between voltage and current across the resistive element, whereas Kirchhoff’s law characterizes the behaviour of current and voltage in an electric circuit.

What is Ohm’s law?

Ohm’s law states that the current flowing through a conductor is proportional to the voltage across it and the other way round for the voltage. 

German physicist Georg Ohm found this principle and the mathematical representation is:


V = IR


The working of Ohm’s law is similar to the flow of water in a pipe. The potential difference between the two ends of the pipe is the same as the current that is driven by the difference in voltage across the resistive element. As the cross-sectional area reduces, the flow of water reduces in the pipe. This is similar to resistance. As resistance decreases, there is an increase in the current.

So, it is understood that Ohm’s law is used for calculating the total resistance across the circuit.

What is Kirchhoff’s law?

German physicist Gustav Kirchhoff was the one to propose Kirchhoff’s law. There are two forms of Kirchhoff’s law:

  • Kirchhoff’s Current Law (KCL)
  • Kirchhoff’s Voltage Law (KVL)

Kirchhoff’s Current Law

KCL states that the total current that enters a node and the total current that flows out of the node are equal. The mathematical representation is:

i1 + i2 = i3 + i4


Kirchhoff’s Voltage Law

KVL states that the sum of all the voltages across the closed loop is zero. The mathematical representation is:

v1 + v2 + v3 + v4 = 0


The other difference between Ohm’s law and Kirchhoff’s law is that Ohm’s law is applicable to a single resistive element while Kirchhoff’s law is applicable to a series of resistive elements. 

Stay tuned with BYJU’S to learn more about other Physics related concepts or subscribe to our YouTube channel for more information.