**1. Introduction**

What do resistors do? The resistors limit the electrical current. To illustrate a simple application: connect a resistor with a LED in series.

The electric current is high enough to make the LED light up, but not high enough to cause damage. In the example above the electrical resistance has the role of limiting the value of the current through LED to a nominal value specific to its use (given by the catalog). At the same time, by limiting the current a potential difference will appear on the electrical resistance inserted with the LED and LED. Both potential additions should give the voltage supply to the circuit, in our case 9V.

Electrical resistance characterizes any electrical conductor. For example, for a homogeneous conductor, the value of the resistance is:

where:

- ρ is the resistivity of the material from which the conductor is made, measured in ohm · meter;
- l is the length of the conductor, measured in meters;
- S is the cross-section of the conductor, measured in square meters.

In an electrical circuit, the value of the resistance is calculated using Ohm's law , being equal to the ratio between the voltage U applied to the source terminals and the intensity I of the current flowing through the conductor. **2. Variation of electrical resistance according to temperature** The ohmic resistance of metals increases with temperature and of coal and liquids decreases as their temperature increases. The electrical resistance of copper increases by 4% at a heating of 10 ° C. How the ohmic resistance of an electric conductor varies with temperature can be determined using the following relation: where:

t2 is the final temperature; t1 is the initial temperature; R2 is the electrical resistance of the material at t2 (final resistance); R1 is the electrical resistance of the material at t1 (initial resistance); α is the temperature coefficient (specific to each material and represents the variation of the resistance of one ohm of the respective conductor to an increase of its temperature by 1 ° C).

**3. The symbol of the electrical resistance**

In the electronic diagrams the symbol of the fixed resistor in the form of rectangle (symbolization according to the European standard IEC) or the symbol "zigzag" (according to the American and Japanese standards) is used.

[adv_1] Resistors are used with converters to form a subsystem of a sensor. Converters are electrical components that convert energy from one form to another, where one form of energy between the two (which is converted, or is to be converted) is electrical. A light dependent resistor, or LDR, is an example of an input converter. Changing the brightness of the light on the surface of the LDR results in changes in its resistance. As I will explain later, an input converter is often connected with a resistor to form a circuit, called a potentiometer. In this case, the voltage of the electrical current coming out of the potentiometer will have a voltage that will reflect the changes of the light that falls on the surface of the LDR from the potentiometer composition.

Microphones and switches are input converters. Speakers, incandescent lamps and LEDs are output converters.

In other circuits, resistors are used to direct the electrical current to certain parts of the circuit or can be used to determine the voltage gain of an amplifier. Resistors are used in conjunction with capacitors to produce delays.

Most electronic circuits need resistors to work well and it is important to find among the dozens of types of resistors available on the one with the correct value, in, or M, for the particular application we want to use.

**4. Fixed value of the resistors **

Figure below shows the construction of a carbon film resistor:

During manufacture, a thin carbon film is placed on a small ceramic bar. The resistive coating is spiraled in an automatic machine until the electrical resistance between the two ends of the bar is as close as possible to the correct value. Metallic bars and ends are added and the resistor is covered with insulation and finally the lines on the insulation are painted to indicate the value of the resistor.

Carbon film resistors are cheap and easy to find, with values of ± 5-10% of their nominal value. "Metal foil and metal oxide resistors are manufactured in a similar method, but have ± 1-2 % of their nominal value There are some differences in the performance of these two types of resistors, but the performance does not affect their use in simple circuits.

Butter coil resistors made by wrapping a wire on a ceramic support. They can be made extremely precise and can be used in multimeters, oscilloscopes and other measuring instruments. Through some types of coil type resistors, strong electrical currents can pass, without overheating the resistor and are used in power sources and other high current circuits.

**5. Color code** How can you find the value of a resistor on the colored strips on it? Each color represents a number, as shown in the table below. The first band on a resistor is interpreted as the FIRST FIGURE of the value of a resistor. For the resistor shown below, the first band is yellow, so the first digit is 4.

The second band gives us the SECOND FIGURE. For the resistor in the image, it is purple, so the second digit is 7. The third band is called MULTIPLICATOR and is not interpreted in the same way as the other 2. It tells us how many zeros we have to add according to the numbers we have. Being red, its value is 2. So the value of the resistor in the image is 4700 ohms, that is 4700 ohms or 4.7kohms.

The remaining band is called TOLERANCE. This was the percentage of the accuracy of the resistor value. Most carbon film resistors have a yellow colored tolerance indicating that it is ± 5% of face value.

When you want to read the value of a resistor, look for the tolerance band, usually yellow, and position it to the right, reading the value of a resistor is not a complicated operation, but requires little practice.

To write this operation as a mathematical equation, we will note the first digit with A, the second with B, the multiplier with N, and the tolerance with X. The formula is: AB x 10 ^{N} ± X%. Color tolerance values are:

**More about color code**

The color code as shown above allows us to find the value of a resistor greater than 100 Ohms. How do we find out the value of a resistor less than 100 Ohms? For 12 Ohms, on the resistor, the first band will be brown, the second red, and the third black. So the first digit will be 1, the second 2, and the multiplier 0 shows that no zero is added to the first two digits.

Now we can indicate any value over 10 Ohms. But how do we proceed to indicate values less than 10 Ohms? For values less than 10, the multiplier will be golden. For example, the colors brown, black, gold (they are in order, from the first band to the multiplier) indicate the value of 1 Ohm, and the colors red, red, gold, indicate the value of 2.2 Ohm. So, if the multiplier is golden, the number of the first and second digits is divided to 10.

Metal sheet resistors, which have a tolerance of ± 1% or ± 2%, often have a code consisting of 4 bands. It works the same way, except that the first three bands are interpreted as numbers, and the fourth as a multiplier. For example, a resistor with a metal sheet of 1 kOhmi has the bands: brown, black, black, brown and brown or red for tolerance.

**E12 and E24 values**

If you have experience in circuit construction, you have noticed that the resistors usually have values of 2.2 kOhmi, 3.3 kOhmi or 4.7 kOhmi and do not have integer values, such as 2 kOhmi, 3 kOhmi, 4 kOhmi etc. Manufacturers do not produce resistors with these values - why? The answer has to do with the fact that resistors are not precisely manufactured, with some tolerance. Look at the table below, which shows the E12 and E24 series values. Resistors are made in multiples of these values. For example: 1.2 ohms, 12 ohms, 120 ohms, 1.2 kOhmi, 12 kOhmi, 120 kOhmi and so on.

We consider the values 100 Ohms and 120 Ohms, close in the E12 series. 10% of 100 Ohms is 10 Ohms, while 10% of 120 Ohms is 12 Ohms. A resistor marked with 100 Ohms and with a tolerance of 10% can have any value between 90 Ohms and 110 Ohms, while a resistor marked with 120 Ohms and the same tolerance can have any value between 108 Ohms and 132 Ohms.

From a practical point of view, all that matters to you is to know that carbon film resistors are available in multiples of E12 and E24. often, for a calculated resistance that you want to use in a particular application, you will need to choose the closest value to the E12 or E24 series.

**6. Limitation of electric current**

You are now ready to calculate the value of a resistor connected in series with an LED. Look at the following figure:

An ordinary LED needs a current of 10 mA and a voltage of 2 V during operation. The power supply of the circuit is 9 V. What is the voltage crossing R1? The answer is 9-2 = 7 V (the voltage passing through the elements of a connected circuit in series must be added to the voltage of the power source).

Now we have two information about the electric current that crosses R1:

- it has the intensity of 10 mA;

- has the voltage of 7 V.

To calculate the resistance, the formula is used:

We substitute the values of V and I:

This formula uses the fundamental units of measurement, ie volts for voltage, amps for intensity and ohms for resistance. In this case, 10 mA had to be transformed into amps, resulting in 0.01 A.

If the value of the current intensity is in mA, the value of the resistance will be in kOhmi:

The calculated value for R1 is 700. What is the closest value in the E12 / E24 series? Resistors with values of 680, 750, and 820 are available. 680 is the ideal choice. This should allow an electrical current with an intensity slightly greater than 10 mA. Most LEDs support electrical currents up to 20 mA, so it's perfect.

**7. Connecting the series and parallel resistors**

In a circuit that contains resistors connected in series, the electric current is the same in all its points. The circuit in the diagram shows 2 resistors connected in series to a 6 V power source.

It does not matter where in the circuit we measure the electric current, it will be the same. The total resistance is given by the formula:

_{Total} R = R _{1} + R _{2}

In our circuit, _{total} R = 1 + 1 = 2 kOhmi. But what intensity will the current passing through it have? The formula is:

**I = V / R = 6/2 = 3mA.**

Note that the current intensity is given in mA, if the replaced resistance is in kOhmi. If the resistor is replaced in Ohmi, then the current intensity will be given in amps.

So through both resistors a current of equal intensity passes. What is the electrical voltage at the terminals of R1? The formula is: V = I * R or U = I * R. Substituting, we obtain: V = 3mA x 1kOhm = 3V

What will be the electrical voltage at the terminals of R2? It will also be 3 V. It is important to note that the sum of the electrical voltages that cross the two resistors represents the voltage of the power supply of the assembly.

The circuit below shows two resistors connected in parallel to a 6V battery.

The circuits with resistors connected in parallel provide alternative paths for the electric current. The total resistance of such a circuit is calculated by the formula:

This is called the product formula over the sum and works for any two resistors connected in parallel. An alternative formula is:

This formula can be expanded to allow multi-resistor calculation, but both formulas are correct. What is the total resistance of this circuit?

The intensity of the electric current can be calculated by the formula:

[adv_1] How is the current in this circuit compared to the current in the circuit with the resistors connected in series? Is bigger. It is more sensitive. By connecting the resistors in parallel and making alternate paths through which the electrical current can pass, it is easier for him to pass there. What is the current intensity that passes through each resistor? Because it is divided, and the resistors have equal values, the electric current passing through R1 will have 6 mA and will be equal to that passing through R2.

The electrical voltage at the resistance terminals R1 is:

**V = I * R = 6mA x 1kOhm = 6V.**

This is equal to that of the energy source. One end of R1 is connected to the anode of the current source and the other is connected to the cathode of the current source. With no other electrical component in the path, the voltage passing through R1 must be equal to that of the current source, ie 6 V. But what is the voltage of the electric current that crosses R2? For the same reason, it is also 6 V.

**IMPORTANT:** When the components (resistors, capacitors, coils) are connected in parallel, the electrical voltage at their terminals is the same.

Below is a slightly more complex circuit, with resistors also connected in series, and in parallel:

To find the total resistance, the first step is to calculate the resistance of the resistors connected in parallel. We know from the calculations made in the above circuit that the total resistance of oxide resistors of 1 kOhmi is 0.5 kOhmi, so the total resistance of the circuit is 1 + 0.5 = 1.5 kOhmi. The intensity of the electrical current of the source is:

**I = V / R = 6kOhmi / 1,5mA = 4mA.**

This is the intensity of the electric current that crosses R1. What is the intensity of the electric current that crosses R2? Since there are two identical paths, on which R2 and R3 are located, through them an electric current with an equal intensity of 2 mA will cool.

The electrical voltage at the resistance terminals R1 is: V = I * R = 4mA x 1kOhm = 4V. Because R _{2} and R _{3} are equal, then the electric currents that cross each one are equal, respectively I _{2} = I _{3} = 2mA. Again, the sum of the electrical voltages on R1 and R _{2} , R _{3 } is equal to that of the power source, in our case of the battery.

**8. Power dissipated by resistors**

When an electrical current crosses a resistor, the electrical energy is converted into heat. This can be seen in an incandescent bulb, in which the electric current flows through the filament, which emits heat and light.

The power of a bulb, a resistor, or any other component, is defined as the power of converting the electric current into light, heat, or any other form of energy. The power is measured in watts (W) or milliwatt (mW) and is calculated by the formula:

**P = U * I = I ^{2} * R = U ^{2} / R**

where P is the electrical power, U - the electrical voltage at the resistance terminals, I - the electrical current that crosses the resistance.

What is the electrical power of a resistor crossed by an electric current of 100 mA current and voltage at 6 V terminals?

**P = U * I = 6V * 100mA = 600mW = 0.6W.**

0.6 W represents the heat generated by the resistor. To prevent overheating, it must have the ability to dissipate heat at the same rate at which it produces it.

The ability of a resistor to dissipate heat depends on its surface. A small resistor with a small surface area cannot dissipate heat quickly enough and it is very likely that it will overheat if strong electric currents pass through it. Larger resistors, with a larger surface area, can dissipate heat more efficiently.

The figure below shows resistors of different sizes.

The power of a carbon foil resistor used in most circuits is 0.5 W. This means that a resistor of this size can lose heat at a maximum rate of 0.5 W. In the previous example, the calculated heat rate loss was 0.6 W, so a larger power resistor of 1 W or 2 W. will be needed. Some resistors are built to allow the passage of very strong electrical currents into the aluminum housing with "fins". "aluminum to increase the surface and dissipate heat more efficiently.

**Bibliography:**

https: //homepages.we...cs/resistor.htm

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