famous German physicist Gustav Robert Kirchhoff (1824 - 1887), a graduate of the University of Konigsberg, as chair of mathematical physics at the University of Berlin, on the basis of experimental data and Ohm's law received a number of rules that allows us to analyze complex electrical circuits.So there were and are used in electrodynamics rules Kirchhoff.
first (rule nodes) is, in essence, the law of conservation of charge in combination with the condition that the charges are not born and do not disappear in a conductor.This rule applies to the nodes of the electrical circuits, i.e.point circuit in which converges three or more conductors.
If we take the positive direction of the current in the circuit, which is suitable to the node currents, and one that moves - for the negative, the sum of currents at any node should be zero, because the charges can not accumulate in the site:
i = n
Σ Iᵢ = 0,
i = l
In other words, the number of charges that correspond to the node per unit time is equal to the number of charges, which go from a given point in the same period of time.
Kirchhoff's second rule - a generalization of Ohm's law and relates to the closed contours branched chain.
In any closed loop, randomly chosen in a complex electrical circuit, the algebraic sum of the products of the forces of currents and resistances of the respective sections of the contour will be equal to the algebraic sum of the emf in this circuit:
i = n₁ i = n₁
Σ Iᵢ Rᵢ = Σ Ei,
i = li = l
Kirchhoff's rules are often used to determine the values of the current strength in the areas of complex circuit when the resistance and set the parameters of the current sources.Consider the application of the rules of procedure of the example of the calculation chain.Since the equations that use the Kirchhoff rules, are common algebraic equations, the number should equal the number of unknowns.If the sample contains a chain of m nodes and n sections (branches), it is the first rule you can make a (m - 1) independent equations, and using the second rule, even (n - m + 1) independent equations.
Action 1. choose the direction of the currents in an arbitrary manner, respecting the "rule" flowing in and out, the node can not be the source or drain charges.If you select the current direction you make a mistake, then the value of this current force will be negative.But the direction of the current sources are not arbitrary, they are dictated by the way the inclusion of the poles.
Action 2. The equation of the currents corresponding to the first Kirchhoff's rule for the node b:
I₂ - I₁ - I₃ = 0
Action 3. write the equations corresponding to Kirchhoff's second rule, but pre-select two independent circuits.In this case, there are three possible options: the left loop {badb}, Right {bcdb} loop and loop around the entire circuit {badcb}.
Since it is necessary to find only three amperage, we restrict ourselves to two circuits.The direction of traversal do not matter, currents and EMF are considered positive if they coincide with the direction of traversal.Go around the contour {badb} counterclockwise equation becomes:
I₁R₁ + I₂R₂ = ε₁
second round commit to a large ring {badcb}:
I₁R₁ - I₃R₃ = ε₁ - ε₂
Action 4. now account for a system of equations, which is quite easy to solve.
Using Kirchhoff's rules, you can do fairly complex algebraic equations.The situation is easier if the circuit contains certain symmetric elements, in this case there may be nodes with the same potential and branch chain with equal currents, which greatly simplifies the equation.
A classic example of this situation is the problem of determining the strength of the currents in a cubic shape, made up of the same resistance.Because of the symmetry circuit potentials of the points 2,3,6, as well as points 4,5,7 will be the same, they can be connected, as it will not change in terms of the current distribution, but the scheme will be simplified considerably.Thus, Kirchhoff's law for circuit Allows easy to perform complex calculation of the DC circuit.
