Laws of Kirchhoff

The laws of Kirchhoff express the Conservation of energy and load in a Electrical circuit. They bear the name of the German physicist which established them in 1845: Gustav Kirchhoff .

In a complex circuit, it is possible to calculate the potential differences at the boundaries of each resistance and the intensity of the D.C. current in each branch of circuit by applying the two laws of Kirchhoff (which rise from the Loi of Ohm): the law of the nodes and the law of the meshs .

Law of the nodes

The algebraic sum of the intensities of the currents which enter by a node is equal to the algebraic sum of the intensities of the currents which leave there.

The intensities of the currents are algebraic sizes (positive or negative). On the figure the direction (arbitrarily selected) currents entering or outgoing is represented of node A.

According to the law of the nodes, one thus has: $i_1 + i_4 = i_2 + i_3 \,$.

For including/understanding this law well, it should be known that the intensity is defined like a flow of load per unit of time $\left(I = \ frac \left\{dq\right\} \left\{dt\right\} \,\right)$. Knowing that the loads cannot accumulate at an unspecified place of the circuit, they circulate, therefore the entirety of the loads which “arrive” at a node sets out again about it.

Law of the meshs

In a unspecified mesh of a network, the algebraic sum of the tensions along the mesh is constantly null

This law rises from the definition of the tension like potential difference between two points. The tension between has and B is U = Vb - Va . Va and Vb being the respective potentials at the points has and B. By adding all the tensions with a mesh and while making use of this definition, one obtains a null result.

Method

1. One traces the direction of path of the current and the tensions associated with each dipole.

2. One draws the mesh.
3. If the direction of the mesh is different from the tension associated with the dipole, it is a negative tension.
4. One replaces in the equation of the meshs.

See too

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