Download Electrical circuits wyklad 2

Dr inż. Agnieszka Wardzińska
Room: 105 Polanka
[email protected]
cygnus.et.put.poznan.pl/~award
Advisor hours:
Monday: 9.30-10.15
Wednesday: 10.15-11.00
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.
Examples
if
R1  R2  R3  R4  R5  1
and U AB  5V
U R1  U AB
R1
1
 5  1V
R1  R2  R3  R4  R5
5
R23  R2  R3  2
R45  R4  R5  2
R23 // R45 
U R1  U AB
R23  R45
 1
R22  R45
R1
1
 5  2.5V
R1  R23 // R45
2
AC voltage divider circuit
 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
and we can write for example UZ1 :
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.
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
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 equation:
Voltage and Current source equivalence
 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
J respectively we can write relations:
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:
 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:
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.