**Resistor definition **– a double-ended, passive electronic component. It is a linear component, which means that the voltage drop is directly proportional to the current that flows through it. Resistor is used to reduce or achieve the desired value of the current that flows in the electric circuit. It can operate under direct, alternating or pulse currents (a type of circuit has a significant impact on its properties). In addition, resistor is a component in which the process of converting electric energy into thermal energy takes place.

A resistor is a insulator-coated resistive material attached to two leads which are utilised to link it into an electric circuit. Depending on the structure, you can find fundamental Kinds of resistors for example:

- carbon – that the Resistive function is done by means of a coating of carbon, and this can be applied to a porcelain tube at the practice of corrosion,
- Metal film – a Coating of metal is employed as a resistance component, which can be deposited on the porcelain tubing in the practice of corrosion,
- foil – the Resistive component here’s a metallic alloy foil wrapped round the insulation body.

Cable (accuracy ) – a Cable with higher resistance is wrapped around a core made from insulator.

**What does a resistor do**

The foundation for understanding the way the resistor operates in an electric circuit is a basic physical phenomenon in electronic equipment and electricity found between 1825 and 1826 with a German math and physics instructor, Georg Simon Ohm. This phenomenon is usually called Ohm’s law.

The Proportionality of current and voltage can be expressed as a formula:

**U = I x R **

Where U is the electric voltage expressed at Volts [V] and that’s the current flowing through the conductor expressed in Amps [A]. We see the proportionality factor is that the resistance R expressed in the unit of ohms [Ω].

Composing this law Concerning the proportionality of current to voltage, we now receive:

**I = G x U**

where I’m the current flowing through the conductor expressed in Amperes [A], U is that the electric voltage expressed at Volts [V], along with also the Proportionality factor is that the conductance G voiced in Siemens [S] That is the reverse of the resistance R.

## Resistor parameters

Like every electronic part, a resistor includes a couple of parameters which explain it. The fundamental ones are resistance and power rating (power reduction ). As you know, resistance is expressed in ohms [Ω]. Resistors are made using resistances from fractions of an ohm into gigaohms (1,000,000,000 ohms). Reduction power expressed in watts [W] will be the greatest allowable energy exerted to a resistor at constant operation along with a temperature under +700C. Typical values vary from thousands of watts. Furthermore, a tolerance (accuracy class) is defined for its resistor. It defines how a true resistance can differ from the nominal resistance given by the manufacturer. The tolerance is defined in [percent ] of their minimal price and can vary from fractions of a percentage around 20 [percent ]. For instance, if a resistor having a nominal resistance value of 220 [Ω] includes a tolerance of 10 [percent ], meaning the producer allows the real resistance value of the resistor to distinguish between 198 and 242 [Ω]! The other parameter of this resistor is that the temperature coefficient of this resistance, which informs how far the value of this resistance varies with temperature fluctuations. In reality, the physical occurrence of current flowing through a conductor is accompanied by the generation of renewable energy. It’s been demonstrated that in conductive substances, there’s a shift in the resistance value of the conductor because the temperature varies. This is the area where theory ends and clinic starts. A resistor is an integral component only in certain simplification and this assumption is adequate in many programs. Returning to the temperature coefficient of resistance, just how can temperature behave to a resistor? The resistance decreases as the temperature rises, according to the attribute below.

The Temperature coefficient of resistance is largely given in [ppm/K]. What’s ppm? It stands for parts per thousand, therefore 1 [ppm] = 1/1000000 = 10-6. If we want to express [ppm] as a percent, we’ve got: 1[percent ] = 10000 [ppm] = 104[ppm]. K] is that the kelvin – that the unit of temperature In an absolute scale: T[K] = t[C] +273.15, therefore such as 373.15K ] 1000C.

## Resistor in series

**Series connection**

The equivalent resistance of the series connection of several resistors “R” is equal to the sum of the resistance of the resistors forming this connection.

**R = R1 + R2 + …Rn**

When many resistors are placed behind another and joined by cables to ensure a possible gap U can be applied to a single and the opposite end of this kind of array of resistors, this type of link of resistors is referred to as a series link. The figure below demonstrates a simple electric circuit comprising an ideal source of electromotive power and resistor in series between factors A and B where the source of SEM keeps a constant potential gap ε.

According to the figure above, charge carriers are able to move into a circuit by just 1 route (no nodes in the circuit), so a current of exactly the identical intensity equal to I have to flow through each resistor.

The resistors in series could be replaced by a replacement resistor with resistance Rz, by which, in exactly the exact potential gap, a current of the exact identical intensity will stream as through every one of the resistors which are a part of this resistor array attached in series. The next figure shows an electrical circuit where the 3 resistors in the preceding figure, are substituted with one identical resistor with resistance Rz.

To derive the expression to compute the resistance Rz of a replacement resistor (substituting the resistors in series) we shall employ Kirchhoff’s second law to the two circuits displayed in the statistics above. Beginning and finishing the analysis point A and moving , we get to the initial circuit:

in turn for a circuit with a substitute resistor Rz:

Since the current I flowing through both circuits takes equal value, therefore, after transforming the above expressions with respect to current I and equating them by sides, we get:

## Resistor in parellel

**Parallel connection**

For two, parallel connected resistors, equation for total combined equivalent resistance is shown below:

**R = R1,2 = R1 * R2 / R1 + R2**

A way of linking resistors would be to join them in resistors in parallel, so i.e. where resistors on a single side and around the opposite hand are linked by shared cables into the ends of that a possible difference U is put on. Joining the resistors this manner causes exactly the exact identical voltage U to be implemented to every resistor, which generates a current of distinct strength at every resistor (in the event of resistors of equivalent resistance, the current flowing through those resistors will clearly have exactly the identical value). Notice that based on the figure below, the current in the SEM source may proceed through several avenues (the current flowing to the node undergoes branching), which warrants the fact of the former announcement.

The possible gap ε (or U ) employed to resistors connected in parallel equal the potential difference across each resistor separately.

As in the instance of resistors in series, we could even replace the parallel resistor with using one equivalent resistor with resistance RZ. Exactly the identical potential difference U is put on the ends of the resistor, leading to a current I equivalent to the amount of these currents generated in all of the resistors connected in parallel.

To derive the formula for calculating the equivalent resistance Rz of resistors in parallel we use Kirchhoff’s first law. Writing this law for a system of resistors connected in parallel will give us.

**I = I1 + I2 + I3**

The currents I1, I2 and I3 flowing through the resistors R1, R2 and R3 respectively, are calculated with the definition of electric resistance. As we wrote previously, the potential difference of the SEM source of ε implemented to a method of resistors connected in parallel equal the potential difference across each resistor separately, so:

By substituting each current into the equation I = I1 + I2 + I3, we get:

A similar equation is obtained for a circuit with equivalent resistance Rz:

Comparing the sides of the two equations above, we obtain:

## Basic equations

**Ohm’s Law**

**R = V / I**

**R** – resistance (Ω – Ohm)**V** – the current between the element ends (V– Volt)**I** – current (A – Ampere)

**Power dissipated on the resistor:**

**P = V * I**

**P **– electric power (W – Watt)

** Note:** More in-depth explanation of Ohm’s Law and more important topics can be found in our

**.**

__911electronic Basic Electronic Course__**Voltage divider**

**Voltage divider** – two resistors in series connection. It is used to separate the voltage supplied to its input, so its output voltage will be the partial input voltage. Input voltage is supplied to the R1 and R2 resistors, while the output voltage is equal to the voltage drop on the resistor R2:

**Vout = Vin * R2/R1 + R2**

## Resistor Division

Memory resistor (that is controlled by current) is called **memristor**. Resistor with adjustable electric resistance is called a **potentiometer**. It is a triple-ended element used as the voltage divider. On the picture below you can find more about resistor’s big family.

## Technical parameters

The most important technical parameters of the resistor are written below:

**nominal resistance**(conductance parameter “G” [S – siemens] is also often used, where G = 1/R) – given by the manufacturer on the housing element that can be measured using a multimeter,**accuracy class(tolerance)**– possible deviation of the actual value of the resistor from the nominal value (given in percentages),**power rating**– the maximum permissible power that can be dissipated as heat from resistor under certain conditions,**temperature coefficient of resistance(TCR)**– it defines resistance variation under the influence of temperature (the smaller the TCR, the more stable resistor is),**voltage limiting**– the maximum value of the DC voltage (or the highest effective value of the alternating current AC), that won’t cause any damage to the component. This value depends on the material from which resistor was manufactured – for popular, low power resistors it ranges from 150 to 500V.

## Resistor Color code chart

I bet that many of you have wondered, what these “colorful stripes” on the resistor actually mean? Below you can find out and “decode” your own resistor’s value.

Let’s take resistor from the Fig. 4. as an example. According to the color chart from Fig. 5., first stripe (purple) has the value of “7”. Second stripe (yellow) has the value of “4”. Third stripe (orange) means the multiplier value, so basically we need to write the first two digits next to each other and multiple that number by 1000 (1k). So, 7 and 4 multiplied by 1000: 74 * 1000 = 74000Ω = = 74kΩ Tolerance of this resistor has the value of +/- 0,05% (grey color).

**Second example:**

**First stripe (green) has the value of “5”. Second stripe (black) has the value of “0”. Third stripe (orange) means the 1k multiplier value.**

5 and 0 multiplied by 1k: 50 * 1000 = 50kΩ. Tolerance of this resistor has the value of +/- 1% (brown color).

**Third example:**

**First stripe (yellow) has the value of “4”. Second stripe (purple) has the value of “7”. Third stripe (brown) means the 10 multiplier value.**

4 and 7 multiplied by 10: 47 * 10 = 470Ω. Tolerance of this resistor has the value of +/- 2% (red color).

That was easy, right?

## Resistor types

**Wire resistors**

A cable resistor, as its name suggests, is made up of a resistance wire wrapped round a body made from ceramic or plastic. The ends of this cable will also be the ends of the resistor. For security, this kind of structure is put in an appropriate housing.

Resistors of the kind, though less and less Frequent, are distinguished by high stability, resistance to Electrostatic discharge, and endurance which may attain ±0.005 percent. But, their endurance, notably temperature, isn’t so significant. Moreover, parasitic parameters like capacitance and inductance May happen on account of the layout. The end effect is a factor impedance Emerging over about 50kHz.

**Thin film resistors**

Thin film resistors are producers’ response to clients who wanted a minimal price. But as is frequently the situation, a fall in quality comes together with a fall in price. Resistors of the kind are created by depositing a thin resistive coating on a ceramic substrate. Such a procedure is quite sensitive to any type of flaws, therefore the resistors made within this technology aren’t characterized by the top parameters, however, their price is rather low.

**Thick film resistors**

Resistors created with this technology will also be one of the most affordable on the industry. But they’ve marginally better parameters compared to thin film resistors. They’re produced by using a paste comprising a ceramic cloth and metallic particles into a ceramic substrate from the practice of screen printing. Afterward, both layers are sintered together, making a completed resistor.

**Foil resistors**

Resistors of the kind are known primarily for their exceptional performance. They’re produced at a photolithography process, through which a resistive course is wrapped in Ni/Cr alloy (chromonickel) foil with a few additives, put on a ceramic substrate. Such a method allows to produce a resistor with superior parameters.

**Resistor ladders**

Even a resistor ladder is just nothing besides many resistors included in 1 housing. This sort of solution, as a result of its size, which makes the positioning of components on the PCB substantially easier. Resistor ladders can be found in both SMD and THT variations, it is also possible to locate them straightened in a DIP situation called the ICs.

**Potentiometers**

A potentiometer is also described among those resistor subtypes. It’s three terminals: involving two of these the value of resistance is constant, the next one is attached with a knob or a slider, so because of that we could correct the value of resistance. There are lots of programs for potentiometers, however, the most frequent are voltage dividers.

**Heating resistors and power resistors**

Heating resistors, and power resistors have a special job – to exude warmth. In the first form the warmth is quite desired, these resistors are usually used as easy heaters. As a result of their small size they’re ideal for heating system e.g. a 3D printer .

Power resistors are distinguished by very Large power They could emit. They are normally cable resistors included in an suitable casing. They are primarily utilised in circuits with higher loading.

Interesting programs of resistors – aside from The traditional software of resistors in digital circuits there Are also a number of intriguing ones explained below.

**Braking resistors**

Braking resistors known primarily in the transport industry are utilized to dissipate heat, and therefore are electricity resistors. They are sometimes discovered at streetcars, cranes, lifts, trains and inverters. As a result of their program, they need to be quite powerful, and the energy that they must dissipate can attain several megawatts.

**Start-up resistors**

In elderly structures, like cranes, overhead cranes and belt conveyors, therefore startup resistors were utilized, that have been substituted with inverters. These were power resistors, generally made from cast iron. Regardless of their displacement from inverters, they continue to be manufactured.

**Grounding resistors**

Grounding resistors are widely utilized in the energy market. They’re utilised to ground the transformer to the impartial stage on one side and also into the working ground on the opposite. Moreover, additionally, there are moderate and low voltage inducing resistors. They’re also employed for earthing the toaster, but they’re located together with a suppression choke, the so called Petersen coil.

**Load resistor**

Load resistors, understood among other folks from the medical and scientific sector, are largely utilized to make an artificial load or to induce a desired current. Hospitals, as an instance, should have emergency power generators. Such devices are exposed to regular inspections, where the loading is simulated by way of proper power resistors.

A common program for terminating resistors is that the Testing of emergency electricity generators, which should be periodically analyzed under load. By utilizing a load resistor, then it’s possible to load the generator at various collections of its own power. Such resistors may be portable, e.g. to a trailer or carried in a van, or static, permanently linked to the generator.

In the latter instance, along with the purpose of Providing a minimal load to your generatorthey also do the role of a resistor efficiency evaluation apparatus, assessing it from time to time. Largely, the load resistors are intended for certain requirements of the client.

Load resistors for labs, technology facilities

– Terminating resistors for water power Plants, gasoline electricity plants,

– Test resistors for generator management channels

– terminating resistors for generators

– Ballast resistors for emergency generating sets

– Discharge resistors to get capacitor batteries.

## Impedance of resistor

When analyzing AC electrical circuits, impedance Z appears. Impedance is a vector quantity. Impedance has three components:

• resistance R [Ω]

• inductive reactance X_{L}=ω·L [Ω]

• capacitive reactance X_{C}=1/(ω·C) [Ω]

The impedance vector is written using complex numbers:

Z=R+j·X_{L}-j·X_{C}

Z=R+j·ω·L>-j·1/(ω·C)

The value of the impedance vector is given by the formula:

Z=(R^{2}+(X_{L}-X_{C})^{2})^{1/2}

Z=(R^{2}+(ω·L-1/(ω·C))^{2})^{1/2}

_{And after performing the subtraction between the inductive reactance XL and the capacitive reactance XC}

Z=(R^{2}+X^{2})^{1/2}

where

• ω=2·π·f – pulsation (circular frequency)[rad/s]

• L – inductance [H]

• C – electrical capacity [F=A·s/V]

• j – imaginary unit→ j^{2}=-1

To calculate the equivalent impedance of the Electrical circuit we Utilize The exact very same principles like resistance except that impedance is really a vector Amount and resistance would be a scalar quantity. After calculating the Equal impedance, the connection between impedance Z and admittance Y is quite beneficial.

Y=1/Z

Z=1/Y

The unit of admittance is Siemens [S].

Admitance also has components

Y=G+j·B

where

• G – conductance [S]

• B – substitution [S]

• j – imaginary unit → j^{2}=-1

In general, we distinguish between two elementary ways of connecting impedances.

– Series connection of impedances → the same current flows through the resistors, the equivalent impedance is equal to the geometric sum of the component impedances.

Z=Z_{1}+Z_{2}+…+Z_{n}

– parallel connection of impedances → the same voltage is applied to the terminals of the component impedances, then the inverse of the equivalent impedance is equal to the geometric sum of the inverses of the component impedances

1/Z=1/Z_{1}+1/Z_{2}+…+1/Z_{n}

When connecting impedances in parallel, it is convenient to use the relationship between impedance and admittance.

Y=Y_{1}+Y_{2}+…+Y_{n}

### The impedance components of Z

Impedance has three components: resistance R, inductive reactance XL, and capacitive reactance XC. Impedance is a vector whose mathematical form is as follows:

Z=R+j·X_{L}-j·X_{C}, where

– R=ρ·l/S

– X_{L}=ω·L

– X_{C}=1/(ω·C)

## Resistor applications

**amplifiers**– as a feedback component,**transistors**– to set the operating point,**signal-filtering devices**– combined with**capacitors**,- widely defined electric circuits.

References:

https://www.budnews.pl/typy-rezystorow-i-ich-zastosowanie-w-nowoczesnym-przemysle/

https://efizyka.net.pl/szeregowe-i-rownolegle-laczenie-rezystorow

https://botland.com.pl/blog/rezystory-oporniki-jak-to-dziala/

Impedancja