**Author: Radoje
Jankovic**

**Introduction**

**When solving,
calculating and analyzing electrical circuits of alternating current of all
voltage levels, industrial and radio frequencies, we almost often encounter the
concept of impedance and admittance. In this article I will cover in detail
almost everything about electrical impedances of all types in such a way that
anyone can understand and easily solve any AC electrical circuit of any voltage
level and frequency**.

**A. What is impedance?**

**In the simplest terms
and understandable to everyone, imedance is a type of more or less complex
electrical resistance in alternating current. A general graphical symbol for
impedance is shown in Figure 1.**

**In Figure 2.a. a graphic symbol with letter
symbols for complex electrical impedance, in Figure 2.b. is shown the graphic
symbol for the same with markings in the polar form.**

**In alternating current electric circuits, the
impedance can only be the ohmic resistance R, only the inductive resistance
(XL) of an ideal coil of inductance L whose ohmic resistance can be neglected,
or only the capacitive resistance (XC) or an ideal capacitor (C) with a
capacity C also of negligible ohmic resistance which we will see in the next
presentation.**

**B. Three Basic Types of Electrical
Impedances-Ideal**

**If impedance Z consists of ohmic resistance R
in ohms, its symbol and label look like in Figure 3.a. According to IEC
standards, the graphic symbol from figure 3.a. is also a graphic symbol for
ohmic (active) resistance, while symbol 3.b. also another form of graphic
symbol for ohmic resistance R.** **Impedance, as well as all electrical quantities
in a complex calculation, are marked with a bold letter Z, or the letter Z with
a dash above the letter or below the letter.**

**When impedance Z consists of pure inductive
resistance XL in ohms, its symbol and label look like in figure 4.a., while the
symbol in figure 4.b. symbol for inductance coil L.**

**When impedance Z consists of pure capacitive
resistance XC in ohms, its symbol and label look like in figure 5.a. while the
symbol in Figure 5.b. designation for capacitor capacity C.**

**C) Four real impedances **

**In practice there are four real impedances, of
which three are incomplete and one is complete impedance. These are: **

**– Inductive impedance graphically shown in
Figure 6. It consists of an active ohmic resistor R and inductance coils L, ZL,
respectively ZRL**

**– Capacitive impedance ZC graphically shown in
Figure 7. It consists of an active ohmic resistor R and a capacitor of capacity
C, i.e. ZRC**

**– The inductive-capacitive impedance ZX is shown graphically in Figure 8. It consists of a coil of inductance L and a capacitor of capacity C, i.e. ZLC.** **In practice, it is also called capacitive-inductive reactance.**

**– Finally, the third , the complete impedance
consisting of an ohmic resistor R, an inductance coil L and a capacitor of
capacity C,** **Figure 9., Z or ZRLC**

**The previous four real impedances have been
discussed in the sense that they consist of only one electrical component each,
the ohmic resistor R, the inductive coil L and the capacitor C. When in
electrical circuit analyzes and practical calculations, each of these three
main electrical components depending on its structures can consist of two or
all three components in the appropriate configuration, and they must be taken
into account during the appropriate calculations.**

**On the other hand,
each electrical component can be connected to each other in series or in
parallel. **

**In Figure 10.a1. and
10.a2. is shown the impedance consisting of one ohmic resistor R and one
winding L which are connected in series and form one total impedance Z or ZRL.**

**In Figure 10.b1. and
10.b2. the same impedance is shown where ohmic resistance R and inductive
resistance XL are ie. windings connected in parallel and which form one total
impedance Z, i.e. ZRL.**

**In Figure 11.a1. and
11.a2. shown is the impedance consisting of one ohmic resistor R and one
capacitor C, i.e. capacitive reactance XC which are connected in series forming
one total impedance Z or ZRC.**

**In Figure 11.b1. and
11.b2. the same impedance is shown where the ohmic resistance R and the
capacitive resistance XC are i.e. of capacitors C connected in parallel and
forming one total impedance Z or ZRC.**

**In Figure 12.a1. and 12.a2. shown is the
impedance consisting of one coil L of inductive resistance XL and one capacitor
of capacity C, i.e. capacitive reactance XC which are connected in series
making one total impedance Z or ZLC. This is actually the pure reactance X or
the total reactance XT of the series connection of the coil and the capacitor.**

**In Figure 12.b1. and 12.b2. is shown the
impedance where the coil L of inductive reactance XL and the condenser of
capacity C of capacitive reactance XC are connected in parallel and which form
one total impedance Z or ZLC or total reactance XT.**

**It should be emphasized here that with these
coil and capacitor connections, the total impedance or reactance can be
positive or negative depending on which component prevails in the total
reactance value.**

**And so we arrived at the fourth and complete
electrical impedance consisting of one ohmic resistor R, one coil L and one
capacitor C which can be connected to each other in series or in parallel which
can be clearly seen in Figure 13. and Figure 14.**

**D. Series impedances**

**In Figure 15.a. series
connections are shown;**

**– ideal ohmic
resistors of different resistance values RT – ZT (a1),**

**– ideal inductive
resistances of different values ZLT – XLT (a2) and**

**– ideal capacitive
resistances – capacitive reactances ZCT – XCT (a3).**

**It should be
emphasized that an unlimited number of the same electrical components can be
connected in series.**

**In Figure 15.b.
ordinal links are shown;**

**– ohmic resistors and
inductive resistances (windings) that make up one total incomplete impedance
ZRLT, resistive-inductive type (b1),**

**– ohmic resistors and
capacitive resistances of capacitors that make up one total incomplete
impedance ZRCT, capacitive-resistive type (b2),**

**– inductive and
capacitive resistances – reactances (coils and capacitors) which also form one
incomplete impedance ZLCT, but therefore form one complete – pure reactance XT,
inductive – capacitive type (b3) and**

**– ohmic, inductive and
capacitive resistances (ohmic resistors, windings and capacitors) that make up one
complete electrical impedance ZT or ZRLCT.**

**E. Parallel impedances**

**Figure 16 shows
parallel connections;**

**– ideal ohmic
resistors of different resistance values RT – ZT (a1),**

**– ideal inductive
resistances of different values ZLT – XLT (a2) and**

**– ideal capacitive
resistances – capacitive reactances ZCT – XCT (a3).**

**It should be emphasized that an unlimited
number of the same electrical components can be connected in parallel.**

**In Figure 17.a.
parallel connections of ohmic resistors and inductive resistances (coils) are
shown, which make up one total incomplete impedance ZRLT, resistive-inductive
type.**

**In Figure 17.b.
parallel connections of ohmic resistors and capacitive resistances of
capacitors are shown, which form one total incomplete impedance ZRCT,
capacitive-resistive type.**

**In Figure 17.c.
parallel connections of inductive and capacitive resistances – reactances
(coils and capacitors) are shown, which also form one incomplete impedance
ZLCT, but therefore form one complete – pure reactance XT, inductive –
capacitive type.**

**In Figure 17.d.
parallel connections of ohmic, inductive and capacitive resistances (ohmic
resistors, coils and capacitors) are shown, which make up one complete
electrical impedance ZT or ZRLCT.**

**F. Combined impedance connections**

**In the case of mixed
or combined connections of different types of electrical components connected
in series or parallel, there are hundreds and thousands of combinations, of
which I will show a few basic ones here.**

**Components (resistors, windings and capacitors)
can be connected to each other in parallel groups of the same components but
also of the same or different values of resistance, inductance or capacity,
and the groups are further connected in series with one or more of the same
components.**

**Also, electrical components can be connected to
each other in parallel groups with several different components, of the same or
different values of resistance, inductance or capacity, and groups connected
in a series with one or more different components, again of the same or
different values.**

**In Figure 18.a. Coils are shown using component
graphic symbols of the same values of inductance, i.e. inductive resistance,
i.e. inductive reactance in a combined connection. Groups with parallel coils are
connected in series with serially connected coils also of the same inductance
value. **

**It should be
emphasized here,**

**yes, even though the
coils have the same inductance values L, their impedances, i.e. inductive
reactances** **have different values due to the way they are connected to each other,
which can be seen in Figure 18.b. ****Total inductive
reactive resistance XLT ie inductive impedance ZLT is shown in Figure 18.c. **

**In Figure 19.a. Coils of different values of
inductance or inductive resistance are shown, i.e. inductive reactance in a
combined connection. Groups with parallel windings connected in a series
(string) with two, three or more coils of different values of inductance L.**

**In Figure 19.b. the equivalent calculation
scheme of this group of inductive reactances after calculating their values
as well as the total reactance of the entire combination of inductances is
presented.**

**In Figure 20.a. shown are capacitors of the
same values of capacity C, i.e. capacitive resistance, i.e. capacitive
reactance in the combined connection, two and three of the same value of
capacitor C connected to each other in parallel and then in series with one,
two or more series capacitors.**

**In Figure 20.b. the equivalent calculation
scheme of this group of capacitive reactances after calculating their values
as well as the total reactance of the entire combination of capacitances is
presented.**

**In Figure 21.a. capacitors of different values
of capacity C, i.e. capacitive resistance, ie. capacitive reactance in the
combined connection, two and three different values of capacitor C connected
in parallel and then in series with one, two or more series capacitors .**

**In Figure 21.b. the equivalent calculation
scheme of this group of capacitive reactances after calculating their values
as well as the total reactance of the entire combination of capacitances is
presented.**

**Figure 22.a. shows a combination of ohmic
resistors R of different resistance values and inductive coils of different
inductance values L. Shown are two parallel groups connected in series, with
two series groups of resistors and coils of different resistance values R and
inductance L. Of course, there can be more than two components.**

**In Figure 22.b. the equivalent calculation
scheme of this group of impedances after calculating their values is shown,
as well as the total impedance of the entire combination of these two
electrical elements. The total impedance of the whole combination can be seen
in Figure 22.c. Everything else is completely clear from the picture.**

**Figure 23.a. shows a combination of ohmic
resistors R of different resistance values and capacitors of different
capacitance values C. Shown are two parallel groups connected in series, with
two series groups of resistors and capacitors of different resistance values
R and capacitance C. Of course, there can be more than two in groups
components. **

**In Figure 23.b. the equivalent calculation
scheme of this group of impedances after calculating their values is shown,
as well as the total impedance of the entire combination of these two
electrical elements. The total impedance of the whole combination can be seen
in Figure 22.c. Everything else is completely clear from the picture.**

**Figure 24.a. shows a combination of coils of
different values of inductance L and capacitors of different values of
capacitance C. Shown are two parallel groups connected in series, with two
series groups of coils of different values of inductance L and capacitor C.
Of course, there can be more than two components in the groups.**

**In Figure 24.b. the equivalent calculation
scheme of this group of impedances is shown, that is, in this case, the
reactance after calculating their values, as well as the total reactance of the
entire combination of these two electrical elements. It should be noted that
certain reactances can be of a positive or negative character, depending on
which of the two predominates. The same applies to the total reactance of this
combination.** **The total impedance of the whole combination can be seen in Figure 24.c.
Everything else is completely clear from the picture. **

**Figure 25.a. shows a combination of resistors,
coils and capacitors of different values of resistance R, inductance L and
capacitance C. Three parallel groups are shown; RL, RC and LC which are
connected in series with coil, capacitor and resistor, again of different
values of inductance L and capacitance C and ohmic resistance R. Of course,
there can be more than two components in groups. In Figure 25.b. the equivalent
calculation scheme of individual reactances of this combination is shown in Figure
25.c. calculation scheme of impedances, of which there are five in this
combination, and at the end, picture 25.d. the total impedance of the whole
combination with all three electrical elements, which means that ZT is the
total impedance. Everything else is completely clear from the picture.**

**And at the end of this consideration of
electrical impedances we have Figure 26.**

**Figure 26.a. shows a combination of resistors,
coils and capacitors with different values of resistance R, inductance L and
capacitance C. Two parallel RLC and two series RLC groups are shown. It is
clear here that it is about four complete electrical impedances because they
are made up of three main electrical components of resistor R, voltage of
inductance L and capacitor of capacity C. In Figure 26.b. the equivalent
calculation scheme of individual reactances of this combination is shown in
Figure 26.c. the calculation scheme of the impedances of which there are four
in this combination, and at the end, picture 26.d. the total impedance of the
whole combination with three electrical elements each, which means that ZT is the
total impedance. Everything else is completely clear from the picture.**

**And, let’s conclude!**

**Plain, clear, simple,
understandable for everyone from student to professional.**