- •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
Harmonic current circuit with series connection of r, l – elements
The ratio for this circuit can be obtained from the expressions of section 4.3.1. in with C . Indeed we get
(4.100)
that is, the capacitance C in Fig. 1.9.a you can replace by the short-circuited jumper. Then, from (4.80) we get
(4.101)
or
(4.102)
From (4.83) we can write down
(4.103)
where
(4.104)
Reactance
(4.105)
Impedance
(4.106)
The phase angle
(4.107)
The current in the circuit and voltages across resistance r and inductance L are defined by the expressions (4.88) - (4.91). The expression for the instantaneous values of the current and voltages are identical with expressions (4.93) - (4.95). In Fig. 4.15 vector diagrams for the voltages and current are shown for the circuit (a) and for the resistances (b).
Fig. 4.15
4.3.3. Harmonic current circuit with series connection of r, c elements
The ratio for this circuit can be obtained from the expressions of section 4.3.1 when L = 0. Indeed we get
(4.108)
that is the inductance L in Fig. 1.9.a you can replace by the short-circuit jumper. Then, from (4.80) we get
(4.109)
or
(4.110)
From (4.83) we can write down
(4.111)
where (4.112)
Reactance
(4.113)
Impedance
(4.114)
The phase angle
(4.115)
The current in the circuit and voltages across resistance R and capacitance C are defined by the expressions (4.88) - (4.90), (4.92). The expressions for the instantaneous values of the current and voltages are identical with expressions (4.93) – (4.94), (4.96). In Fig. 4.16 presents vector diagrams for the voltage and current are shown for the circuit (a) and resistances (b).
Fig. 4.16