Kirchhoff Current Law and Kirchhoff Voltage Law

Kirchhoff’s Laws

Kirchhoff’s laws relate the currents and voltages in the branches of an electrical circuit. Those relationships are the Kirchhoff laws, or more specifically the Kirchhoff Current and Voltage laws. KCL balances current at a junction. KVL balances voltage around a closed loop. Together they give the equivalent electrical resistance or AC impedance of a network and the current in each branch. Gustav Robert Kirchhoff first stated the laws, so they are also called Kirchhoff Laws.

Kirchhoff’s Current Law

In an electrical circuit, current is a conserved quantity.
At any point the total current that enters equals the total current that leaves. That point can be anywhere in the circuit, including a simple point on a wire or a junction of several branches.

If the point sits on a conductor that carries current, the current that enters the point also leaves it. The same balance holds at a junction of several branches.

The total current that enters a junction equals the total current that leaves it. Kirchhoff Current law, also called Kirchhoff First Law, states that the algebraic sum of the branch currents at any junction is zero. Take currents entering the junction as positive and currents leaving as negative. Those signed currents then add to zero.
The mathematical form of Kirchhoff’s Current Law is as follows.
n branches meet at the junction.
Let

The currents in branches 1, 2, 3 …. m enter the junction.
The currents in branches leave the junction.
Currents in branches 1, 2, 3 …. m are therefore taken as positive, and currents in branches are taken as negative.
The signed branch currents at the junction are

Their sum at the junction is

That sum is zero by Kirchhoff Current Law.
Therefore,
The compact form of Kirchhoff First Law is ∑ I = 0 at any junction of an electrical network.

Video Presentation of Kirchhoff’s Current Law – Basic Theory

Kirchhoff’s Voltage Law

This law deals with voltage drops around a closed path. Start at one point on a loop. The potential can change as you move from element to element. When you return to the starting point, the potential is the same as when you left. The net voltage rise around the loop therefore equals the net voltage drop. That statement is Kirchhoff’s Voltage Law, also called Kirchhoff’s Second Law.

Take voltage rises around the loop as positive and voltage drops as negative, and their algebraic sum is zero. Suppose n elements in series form a closed loop. Of those elements, m are a voltage source and n – m are dropping elements such as resistors.
The source voltages are
The resistor drops are
With rises taken as positive and drops as negative, the signed voltages around the loop are

By Kirchhoff Voltage law their sum is zero.

So Kirchhoff Second Law is ∑V = 0.

Application of Kirchhoff’s Laws to Circuits

To find how current divides in a circuit, write Kirchhoff’s Current Law at the junctions. Then write Kirchhoff’s Voltage Law around each loop. Solving that set of equations gives the unknown currents, voltages and resistances.

Some Popular Conventions We Generally use During Applying KVL

1. The resistive drops in a loop due to current flowing in clockwise direction must be taken as positive drops.
2. The resistive drops in a loop due to current flowing in anti-clockwise direction must be taken as negative drops.
3. The battery emf causing current to flow in clockwise direction in a loop is considered as positive.
4. The battery emf causing current to flow in anti-clockwise direction is referred as negative.