Equivalent Generator Method

The equivalent generator method is a method of converting electrical circuits in which circuits consisting of several branches with EMF sources are reduced to one branch with an equivalent value.

Application

The equivalent generator method is used in the calculation of complex circuits in which one branch is allocated as the load resistance, and it is required to study and obtain the dependence of the currents in the circuit on the value of the load resistance.

In accordance with this method, the invariable part of the circuit is converted to a single branch containing the EMF and internal resistance of the equivalent generator.

Applying the Equivalent Generator Method

EMF of the equivalent generator is determined by the formula:

$E_{eqv}={\frac {\sum _{i=1}^{n}{E_{i}G_{i}}}{\sum _{i=1}^{n}{G_{i}}}}={\frac {{E_{1}G_{1}}+{E_{2}G_{2}}+{E_{3}G_{3}}+\ldots +{E_{i}G_{i}}}{G_{1}+G_{2}+G_{3}+\ldots +G_{i}}},$ ${\ displaystyle E_ {eqv} = {\ frac {\ sum _ {i = 1} ^ {n} {E_ {i} G_ {i}}} {\ sum _ {i = 1} ^ {n} {G_ {i}}}} = {\ frac {{E_ {1} G_ {1}} + {E_ {2} G_ {2}} + {E_ {3} G_ {3}} + \ ldots + {E_ { i} G_ {i}}} {G_ {1} + G_ {2} + G_ {3} + \ ldots + G_ {i}}},}$

Where: $G_{i}$ ${\ displaystyle G_ {i}}$ - the conductivity of the circuit, equal ${\frac {1}{R_{i}}}.$ ${\ displaystyle {\ frac {1} {R_ {i}}}.}$

To determine the equivalent resistance of the generator, the calculation of series and parallel connected resistances is used , and also, in the case of more complex circuits, the triangle-star transformation is used.

After determining the parameters of the equivalent generator, it is possible to determine the current in the load at any value of the load resistance according to the formula:

$I_{H}={\frac {E_{eqv}}{R_{eqv}+R_{H}}}.$ ${\ displaystyle I_ {H} = {\ frac {E_ {eqv}} {R_ {eqv} + R_ {H}}}.}$

Any arbitrarily complex active two-terminal can be represented by an equivalent generator whose emf is equal to the open circuit voltage at the terminals of the two-terminal, and the internal resistance is equal to the input resistance of the passive two-terminal from the same terminals. When determining the input resistance, all sources must be replaced by their internal resistances - the EMF sources are shorted and the current sources open.

Literature

Bessonov L.A. Theoretical Foundations of Electrical Engineering. Electrical circuits. 2002. - ISBN 5-8297-0026-3

Equivalent Generator Method

Application

See also

Literature

More articles: