- •4.1. The basic laws of the electrical engineering
- •4.2. Equivalent transformations in electric circuits
- •4.2.1. Series connection of elements
- •4.2.2. Parallel connection of elements
- •4.2.3. Mutual equivalent transformations of the parallel and series connection of elements
- •4.2.4. The transformation of delta – to star – connection and back
- •4.2.5. Conversion circuits with the ideal voltage and current sources
- •4.3. The simplest harmonic current circuit
- •4.3.1. Harmonic current circuit with series connection of r , l , c elements
- •Harmonic current circuit with series connection of r, l – elements
- •4.3.3. Harmonic current circuit with series connection of r, c elements
- •4.3.4. Harmonic current circuit with a parallel connection of r, l, c elements
- •4.3.5. Harmonic current circuit with a parallel connection of r, c elements.
- •4.3.6.Harmonic current circuit with a parallel connection of r, l elements
- •4.4. Inductive - coupled circuit
- •4.4.2. Series connection of the magnetic - coupled coils
- •4.4.3. Parallel connection of magnetic coupled coils
- •4.4.4. Notion of the ideal and the real transformers
- •4.5. The of calculation methods of harmonic current circuits
- •4.5.1. Features of harmonic current circuits calculation
- •4.5.2. The equivalent complex circuit
- •4.5.3. Method of Kirchhoff's equations
- •4.5.4. The method of loop currents
- •4.5.5. Method of the nodal voltages
- •4.6. The main theorem of the circuit theory
- •4.6.1. Superposition theorem
- •4.6.2. Theorem on the equivalent generator
- •4.6.3. Reciprocity theorem
- •4.6.4. Compensation theorem
- •4.6.5. Thellegen theorem
- •4.7. The optimal methods of electrical circuits calculation
4.2. Equivalent transformations in electric circuits
Two sites of the electric circuit are called equivalent if the replacement of one by a new one the currents and voltages in the rest of the circuit will not change.
When calculating the electric circuit it is necessary to formulate and to solve a of linearly independent equations system of electrical balance. Equivalent transformations of electrical circuits are based on equivalent transformations of the corresponding equations system of electrical balance.
4.2.1. Series connection of elements
Let us consider an electrical circuit with a serial connection active resistances r , r ,..., r , inductances L , L , ..., L , capacitances C , C ,..., C and voltage sources with the EMF e , e , ... e (Fig.4.1).
Fig. 4.1
According to the law of Kirchhoff’s low for the voltage we get for the instantaneous values
(4.18)
or
(4.19)
and finally
(4.20)
where:
(4.21)
(4.22)
(4.23)
(4.24)
I.e. by a series connection of resistances or inductances the equivalent resistance or inductance equals to the sum of series-connected resistances or inductances.
By a series connection capacitances the value of inverse equivalent capacitance equals to the sum of the inverse values of each series connected capacitances.
By a series connection of the voltage sources value of equivalent voltage source equals to the algebraical sum of the values of each of series-connected voltage source.
Serial connection ideal current sources is impossible.
Similar relations can get for complex resistances and EMFs
(4.25)
On the rules of a serial connection elements is based device voltage divider (Fig. 4.2)
Fig. 4.2
Here
(4.25.а)