1. Dr inż. Agnieszka Wardzińska Room: 105 Polanka agnieszka.wardzinska@put.poznan.pl cygnus.et.put.poznan.pl/~award Advisor hours: Monday: 9.30-10.15 Wednesday: 10.15-11.00

2. Voltage divider circuit When the resistors are connected in series, the voltage is divided proportionally to the resistor values: The equation for voltage divider circuit works for passive circuits fragments. There is no limit for the number of resistors connected in series. The numerator should consist of multiplication of the total voltage (of the resistors in series) and resistance where we want to calculate the voltage drop, in the denominator sum of resistors connected in series.

3. Examples

4. Similarly as for DC circuits we can write the voltage and current dividers laws, but in place of resistors we will have the impedance. Then when the impedances are connected in series, the voltage is divided proportionally to the impedance values AC voltage divider circuit and we can write for example U Z1 :

5. Current divider circuit When the resistors are connected in parallel, the current is divided proportionally to the resistor values. Thy formula presented below are particularly usefull for two resistances circuit but it is often possible to construct the two elements circuit from more elements circuit. That is important to remember, the presented formulas are valid only for fragment of circuit with passive elements. If the analyzed branch contains the active element it is not possible to consider it as current divider circuit.

6. Current divider circuit In particular, when a parallel circuit is composed of more identical resistances, the current is divided equally between all the branches, e.g. in four branches: EXAMPLES

7. AC current divider circuit Similar as for DC when the impedances are connected in parallel, the current is divided proportionally to the complex impedance values. The formula presented below are particularly usefull for two impedances circuit but it is often possible to construct the two elements circuit from larger passive circuit.

8. Voltage and Current source equivalence The real voltage source can be replaced by real current source in an easy way. The sources are equivalent. Below there is prezented the voltage source and equivalent current source and formulas to convers one to another. The resistance in voltage and current equivalent sources are the same The equivalent voltage source value E, when converting from current source is calculated from equation: The equivalent current source J, when converting from voltage source is calculated from equation:

9. In equivalent circuits the voltage U and current I are equivalent only for nodes A and B. There is important to remeber that the current I is the sum of currents in branches of current source: and the voltage U is the sum of voltage on Rs and E (taking into account the direction of the voltage drops): Circuit with Δ or "Y" conections can be simplified to a series/parallel circuit by converting it from one to another network. After voltage drops between the original three connection points (A, B, and C) have been solved for, those voltages can be transferred back to the original circuit, across those same equivalent points. Voltage and Current source equivalence

10. AC Voltage and Current source equivalence The voltage source with series impedance can be replaced by current source with parallel impedande in an easy way (as for voltage and current real source, see 2.1.6). The sources are equivalent. Below is the general rule, and examples of the use of the circuit is just a resistor, a coil or capacitor. The general rule: Analogously as in DC the impedance for current and voltage source will be the same, and for the equivalent voltage source value E and equivalent current source value J respectively we can write relations:

11. Then the impedance for current and voltage source will be the same: and for the equivalent voltage source value E and equivalent current source value Jrespectively we can write relations: Similarly for the capacitor we can write: When the impedance has only resistance character, then the voltage and current sources has the same phase shift. For the coil given as impedance Z we can redraw the sources as below:

12. Maximum Power Transfer Theorem Maximum Power Transfer Theorem states that the maximum amount of power will be dissipated by a load if its total resistance Rl is equal to the source total resistance Rs of the network supplying power. For maximum power: The Maximum Power Transfer Theorem does not assume maximum or even high efficiency, what is more important for AC power distribution.