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Resistors

Introduction

Resistors are the most commonly used components in the electronic circles. They convert the electric energy passing through them into heat in order to "adjust" electricity and voltage by matching the components in the rest of the circuit. These changes can be explained by some basic electronic laws such as Ohm's law and first and second Kirchoff's law.

DSC_4573
low power resistors from Set resistor400

Ohm's law

Resistance is the basic property of the resistor, and the dependence between the resistor sizes, voltage and the electricity passing through the resistor is defined by Ohm's law:

I = frac{V}{R} quad text{or}quad V = IR quad text{or} quad R = frac{V}{I}. [Ω]

where:

  • U - voltage measured in Volts [V]
  • I -  electricity measured in Amps [A]
  • R - resistance in Ohms [Ω]

Ohm's law applies to any other component, not just resistors, because each component has its resistance(even if its very small).

So, measuring unit for resistance is Ohm, the symbol is Greek letter omega [Ω], and it was named after German physicist Georg Ohm.
Now, let's look at a simple electric circuit seen in the picture below. If the amount of voltage of a source in the picture is U = 1V, and the amount of resistance R = 1Ω then the amount of electricity is equal to I = 1A.

sk

LED diode and the resistor

When talking about LED diodes and Ohm's law, me must assume that LED diode, as a consumer, also has its resistance (as we have already said, each component has its resistance). For LED diode we usually take that it uses 20mA per 2.5V, so we can easily calculate its resistance:  R = U/I = (2.5)/(0.02) = 125Ω.
The amount of 2.5V is approximate and depends on the wavelength of the diode, for more check the LED diode tutorial.
Let's say we want to use LED diode with 5V we have available on the Croduino. The total resistance of the circuit should be: Ruk = U/I = (5)/(0.02) = 250Ω. Resistors should be a total of  250Ω minus the LED diode resistance of 125Ω, so R =125Ω. We can assume that the current for the entire electric circuit, for both the LED and the resistor, is equal to 20mA because the components are serial-connected.

The same calculation for the value of the resistor could be made if we counted the voltage on the resistor only. We know that the source voltage is 5V(Croduino), and the LED consumes 2.5V. If we deduct it, Uiz - Uled = 5V - 2.5V = 2.5V, we are left with 2.5V which need to be "consumed" on the resistor. Let us apply the Ohm's law on the resistor, we know that the current is 20mA, R = Ur / I = 2.5V / 0.02 = 125Ω.

resistor

We shall use the closest resistor of 220Ω. According to the Ohm's law, the voltage of the resistor is equal to: U = I ⋅ R = 0.02 ⋅ 220 = 4.4V. Since the source voltage is 5V, for our LED we are only left with: Uled = Usource - Ur = 5V - 4.4V = 0.6V. It is not something, right? If we assume that the current remains the same(but it does not because of the LED's characteristics), LED's resistance is Rled = Uled / Iled = 0.6V / 0.02 = 30Ω. 

Luckily, we know that the current passing through the LED won't remain 20mA at the voltage of 0.6V, but will be very close to zero. It is simply because of the LED's characteristics (LED is a semiconductor). You can find out more about it in some other datasheets about LED diodes or another tutorial about semiconductors and diodes.

Resistor value reading

When using a resistor it is necessary to know the amount of its resistance and the maximum amount of dissipation power. The resistance amount is indicated on the resistor and most commonly with four or five colored rings. Each color of the ring stands for a certain value and meaning, which can be seen from the picture:

1

The picture shows how the 120kΩ resistor looks like. The first ring is brown, the second red, the third is yellow and the last one gold.

  • first digit - brown = 1
  • second digit - red = 2
  • potency - yellow = 10.000
  • tolerance - gold = 5%

The amount of 120k is obtained by writing down the first and second digit and multiplying it for potency. So, 12 x 10,000 = 120,000 or 120k.

2

The maximum dissipation power a resistor can withstand is the power that can be developed on the resistor in form of heat, and which does not destroy it (literally happens to burn). Value data for individual resistors should be found in the manufacturer's datasheets. The most commonly used are so-called low power resistors, both in the Beginner's set or Resistor's set 400, and are 1 / 4W or 0.25W. This means that at the 5V voltage the maximum allowed current is: I = P / U = 0.25 / 5 = 50mA.

Serial circuit of the resistor

ser

The resistor connection seen in the picture is referred to as a serial connection. The basic characteristic of this compound is that we have one current flowing through both resistors, generating a voltage drop. The total resistance of the serial resistor compound is equal to the sum of the individual. R = R1 + R2.
The source voltage U is divided into both resistors at a ratio equal to the ratio of their resistances. This means that in the case where R2 is twice as large as R1, and the supply voltage is equal to the voltage drop at R2 it will be two times larger than the drop on R1 and their sum equal to the U supply voltage. In the form of an equation we can write it down as: R2 / R1 = U2 / U1.

Where U1 and U2 stand for voltage drops on the R1 or R2 resistor. The sum of voltages U1 and U2 is equal to the supply voltage U: U = U1 + U2.
Therefore, the serial connection is also called a voltage divider because it divides the voltage supply into a ratio equal to the ratio of resistance.
If we have a 4.5V voltage battery, and we need a 1.5V voltage then we can use a serial connection of two resistors.
The values of resistance are calculated according to the above formula: R2 / R1 = U2 / U1 = 1.5 / 3 = 0.5. This means that if R1 takes 2kΩ, then R2 must be 0.5 * R1 = 1kΩ.

Paraller resistor connection
par

The total resistance of the parallel circuit of two resistors is equal to:
1 / R = 1 / R1 + 1 / R2.

The basic characteristic of a parallel circuit is that, unlike in the serial, we have one voltage arranged on both resistors. Nevertheless, now we have two currents that run each through its own resistance. The ratio of their strength is inversely proportional to the ratio of resistance through which they flow: I1 / I2 = R2 / R1. Where I1 stands for current through R1 resistor, and I2 current through R2. The sum of the current I1 and I2 is equal to the total current I:
I = I1 + I2. For this reason, the parallel circuit of the resistor is also called the current divider.

If for any reason we need to divide the current of 3A into two currents at a ratio of 2: 1, we will use a parallel resistor connection. Resistance ratios will be calculated according to the formula below:
R2/R1 = I1/I2 = 2/1 =2. If we take a value of  for R1 resistor, then R2 is equal to 2*R1=10Ω.

If in the parallel connection we have an n of equal resistor (R1 = R2 = ... = Rn), then total resistance can be calculated according to the formula: R = R1 / n. This means that a resistance of 1kΩ can be achieved by connecting two 2kΩ resistors in a parallel.

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