Electrical Circuits
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: 10.15-11.00Voltage 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
Examples
V R R R R U U R R R R R R R R R R R R AB R 2.5 2 1 5 // 1 // 2 2 45 23 1 1 1 45 22 45 23 45 23 5 4 45 3 2 23 V U and R R R R R if AB 5 1 5 4 3 2 1 V R R R R R R U UR AB 1 5 1 5 5 4 3 2 1 1 1
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
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
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:
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.
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
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.
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
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:
