Kirchhof's Law

Kirsof law allows us to solve complex circuit problems by defining a number of basic network laws and theorems for voltages and currents around a circuit.

In our series of resistors, we found that when two or more resistances are connected in series, parallels or combinations of both, a single equivalent resistance (R T) can be found and these circuits comply with the Ohm Act.

kirchhoff law
Kirsof Law

However, sometimes in complex circuits such as bridges or T networks, we cannot use only the Ohm Act to find voltages or currents circulating in the circuit.For such calculations we need certain rules that allow us to obtain circuit equations, and for this we can use kirsof law .

In 1845, the German physicist Gustav Kirchhoffdeveloped a pair or a set of rules or laws that deal with the preservation of current and energy in electrical circuits.These two rules are generally known as: One of the Kirchhoff laws regarding the current flowing around a closed circuitKirsof Circuit Laws,Kirsof Current Law, (KCL) and other laws concern voltage sources in a closed circuit,Kirsof VoltageThe law, (KVL) .

Kirsof First Law – Akin Law, (KCL)

Kirchhoffs Current Law, or KCL, states that "the total current or load entering a connection or node is exactly equal to the load that leaves the node, as no load is lost within the node, and has nowhere else to go but to leave."In other words, the algebraic sum of ALL currents entering and exiting a node must be equal to zero, I (output) + I (input) = 0. Kirchhoff's idea is widely known as The Protection of the Load.


Kirsof Current Law

kirchhoff law

Here, the three currents entering the node, I 1 , I 2 , I 3 , two currents separated from the node as a value, I 4 and I 5 , are negative in value.Then it means that we can rewrite the equation as follows;

I 1 + I 2 + I 3 – I 4 – I 5 = 0

The term node refers to an electrical circuit, in general, two or more current carrier paths or a connection or merger of elements as cables and components.There must also be a closed circuit path for the current to flow in or out of a node.We can use Kirchhoff's current law to analyze parallel circuits.

Kirsof's Second Law – TensionLaw, (KVL)

Kirchhoffs Voltage Law, or KVL, states that " in any closed loop network, the total voltage around the loop is equal to the sum of all voltage drops within the same loop", which is equal to zero.In other words, the algebraic sum of all voltages in the loop must be equal to zero.Kirchhoff's idea is known as the Conservation of Energy.

Kirsof Tension Law

kirchhoff law

Continue in the same direction, starting from any point in the cycle, noting the direction of all voltage drops, positive or negative, and returning to the same starting point.It is important to maintain the same direction clockwise or counterclockwise, otherwise the last voltage total will not equal zero.We can use Kirchhoff's voltage law to analyze serial circuits.

When analyzing DC circuits or AC circuits using Kirsof Circuit Laws, a number of definitions and terminologies are used to identify the circuit parts analyzed, for example: nodes, paths, branches, loops and networks.These terms are often used in circuit analysis, so it is important to understand them.

Common DC Circuit Theory Terms:

  • • Circuit – a circuit is a closed loop conductive path through which an electric current flows.
  • • Path – a single line of fasteners or resources.
  • • Node – a node is a connection, connection, or terminal within a circuit that is formed by connecting or merging two or more circuit elements to form a port between two or more branches.A node is indicated by a period.
  • • Branch – a branch is a single group of components or components, such as resistors or a resource that connects between two nodes.
  • • Loop – loop is a simple closed path in which no circuit element or node is encountered more than once in a circuit.
  • • Network (Mesh) – the network is a single closed loop series path that does not contain other paths.There are no nooses in a net.

In addition:

If the same current value passes through all components, it is said that the components are connected to each other in Series.

It is said that the components are connected in parallel if they have the same voltage between them.

A Sample DC Circuit

kirchhoff law

Kirsof Law Question Example 1

Find current flowing from 40Ω resistance, R 3

kirchhoff law

There are 3 arms, 2 nodes (A and B) and 2 independent loops in the circuit.

Kirchhoff Current Law , KCL equations:

On node A : I 1 + I 2 = I 3

On node B : I 3 = I 1 + I 2

Kirchhoff Voltage Law , KVL equations:

Cycle 1 is given as follows: 10 = R 1 I 1 + R 3 I 3 = 10I 1 + 40I 3

Cycle 2 is given as follows: 20 = R 2 I 2 + R 3 I 3 = 20I 2 + 40I 3

Cycle 3 is given as follows: 10 – 20 = 10I 1 – 20I 2

Since I3 is the sum of I1 and I2,we can rewrite it:

Equation 1: 10 = 10I 1 + 40(I 1 + I 2 ) = 50I 1 + 40I 2

Equation 2: 20 = 20I 2 + 40(I 1 + I 2 ) = 40I 1 + 60I 2

We now have two "Synchronous Equations"that can be reduced to give us I 1 and I 2 values.

I 2 in I 1 gives us -0.143 Amps

I 1 in I 2 gives us 0.429 Amperagevalue.

So : I3 = I1 + I2

Current passing through R3 resistance: -0.143 + 0.429 = 0.286 Amps

and the voltage calculated on resistance VR3 = 0.286 x 40 = 11.44 volts

The negative sign for I 1 means that the direction of the initially selected current flow is incorrect, but never a problem.In fact, the 20v battery charges the 10v battery.

Implementation of Kirsof Circuit Laws

  • 1.Assume that all voltages and resistors are given.( V1, V2,… If it does not label R1, R2, etc.)
  • 2.A current flows into each branch or network (clockwise or
  • 3.Label each branch with a branch current.(I1, I2, I3, etc. )
  • 4.Find Kirchhoff's first-law equations for each node.
  • 5.Find Kirchhoff's second legislative equations for each of the circuit's independent cycles.
  • 6.Use linear concurrent equations as needed to find unknown currents.

In addition to using kirsophobic laws to calculate the various voltages and currents circulating around a linear circuit , we can also use cycle analysis to calculate currents in each independent cycle, which only helps to reduce the amount of mathematics required using kirchhoff laws.In the next lesson about DC circuits, we will look at Mesh Current Analysis to do just that.