**What is a Resistor?**

Resistors are electronic components with a specific never changing electrical resistance which limits the flow of electrons through a circuit. They are a critical piece in almost every circuit and they play a major role in our Ohm’s Law Equation that we covered in our previous chapter.

*Take a look at the previous Tutorials;*

**Lesson 1**: Electricity and how it works

**Lesson 2**: Circuits basics – Open Vs Closed

**Lesson 3**: Current – AC Vs DC

**Lesson 4: **Resistance, Voltage and Current & Ohm’s Law

Resistors are known to be passive components which means they can only consume power and can’t generate it. They are commonly used to divide voltage, limit current and are often added to circuits to complement other active components such as Op Amps and other integrated circuits.

**Units of Resistance:**

In the previous chapter, we saw that the electrical resistance of any resistor is measured in “** Ohms**” whose symbol is represented by the Greek capital-omega, Ω and we also defined 1Ω as the resistance between two points where 1Volt (1V) of potential energy will push 1Ampere (1A) of current. To make large values of resistance easier to read, it’s very common to see resistors in kilohm (kΩ), megaohm (MΩ) e.g. 3,500Ω can be represented as 3.5kΩ and a 7,500,000Ω can be written as 7.5MΩ.

**Schematic Symbol:**

All resistors have only two terminals, one on each end of the resistor and it’s these terminals that connect to the rest of the circuit. When simulating circuit schematics, resistors are often represented by one of these two schematic symbols.

*Fig 1. The common resistor schematic symbols.*

Resistors on a circuit are commonly represented with a resistance value and a unique name usually an *R* preceding a number for-instance *R1*. The resistor value displayed in *Ohms (e.g 2kΩ)* is important for evaluating and the overall construction of the circuit. Below is an illustration of a resistor in a simple circuit…

*Fig 2. In this circuit, a resistor limits the current through an LED.*

* *

**Types of Resistors:**

Resistors are of different shapes and sizes, they come in one of two termination types i.e. through-hole and surface-mounted. Resistors can be a standard, static resistor or a special variable resistor.

**1 – Through-Hole (Plated through-hole):**

These resistors are usually more useful in breadboarding, prototyping or in any situation where you would rather not solder tiny SMD resistors. They come with long leads which are stuck into a breadboard or hand-soldered onto a prototyping board or PCB. The long leads are often trimmed and such resistors take-up much more space than their surface-mounted counterparts.

**2 – Surface-Mount-Device or Technology (SMD/SMT):**

This type of resistors are intended to sit on top of PCBs where they are soldered onto mating landing pads. They are usually tiny black rectangles terminated on either side with even smaller, shiny conductive edges often set into place by a pick-&-place robot and sent through an oven where the solder melts and holds them in place as shown below. These are great for mass circuit-board-production and also in circuit designs where space is limited.

In both resistor types, a small film of resistive metal alloy is sandwiched between a ceramic base and a glass/epoxy coating and then connected to the terminating conductive edges.

**Other types of Resistors:**

Not all resistors are static, there are also variable resistors such as ** potentiometers** and

**. Pots connect two resistors internally, in series and adjust a center tap between them creating an adjustable**

*rheostats***voltage divider**. Rheostats are resistors that can be adjusted between a specific range of values.

Variable resistors are often used for inputs for-example volume knobs which are adjusted for a desired volume as shown in the figure below.

**How to read Resistor Values:**

Most resistors are marked to show what their resistance is. SMD resistors have their own value-marking system whereas PTH resistors use a color-coding system which requires decoding for one to know the resistance.

**Decoding color bands on PTH Resistors:**

Through-hole axial resistors will either have four, five or six bands of color circling the resistor. For us to find out the resistance of a given resistor, we need to decode the colors printed on the resistors body and this varies for based upon the number of color bands on the resistor.

**Four – Band color resistor:**

For a **FOUR **color band resistor, the first two bands indicate the *two most significant digits* of the resistor’s value. The third band is a weight value which *multiplies *the two significant digits by a power of ten. The final band indicates the tolerance of the resistor.

Tolerancebasically explains how much more or less the actual resistance of the resistor can be compared to what its normal value is. Resistors with a low tolerance have a low variation in resistance whereas Resistors with a high tolerance have a high variation in the resistance. For-example, a 2kΩ resistor with a 5% tolerance could actually be anywhere between 2.95kΩ and 2.05kΩ.

**Example:**

Qn.

*Given a four color band resistor with the color code Red, Black, Red and Gold as shown in the image above. What is the Resistor Value?*

**Solution:**

When decoding the resistor color bands we use a resistor color code table which shows each of the colors and which value, multiplier, or tolerance they represent.

Consider the table below for a 4 color band Resistor:

For the first two bands, we find the color’s corresponding digit value. The given Resistor has **Red** and **Black** to begin with – which have digits 2 and 0 ie (20). The third band is also **Red** which indicates that 20 should be multiplied by 100 that is 20 times 100 which is 2000 or **2kΩ**

**Therefore; The resistor value of the given resistor in question is 2kΩ with a tolerance of +/_ 5%.**

**Five-Band color resistor:**

For a **FIVE** color band resistor, this has 4 bands on the left side and one band on the right side. The first three bands (Band 1, Band 2 & Band 3) indicate the 1^{st}, 2^{nd}, & 3^{rd} significant values of the resistor. The 4^{th} band color is the decimal multiplier whereas the 5^{th} band color indicates the Resistor Tolerance.

**Example:**

Qn:

*Given a five color band resistor with the color code Green, Blue, Black, Red and Gold as shown in the image above. What is the Resistor Value?*

Solution:

Consider the table below for a 5 color band Resistor:

For the first three bands, we find the color’s corresponding digit value. The given Resistor has **Green**, **Blue** and **Black** to begin with – which have digits 5, 6 and 0 ie (560). The forth band is **Red** which indicates that 560 should be multiplied by 100 that is 560 times 100 is 56000 or **56kΩ. **The fifth band is **Gold** which indicates a tolerance of +/- 5%

**Therefore; The resistor value of the given resistor in question is 56kΩ with a tolerance of +/_ 5%.**

**Six – Band color Resistor:**

For a **SIX** color band resistor, this has 4 bands on the left side and two bands on the right side. The first three bands (Band 1, Band 2 & Band 3) indicate the 1^{st}, 2^{nd}, & 3^{rd} significant values of the resistor respectively. The 4^{th} band color is the decimal multiplier. On the right side, the 5^{th} band color indicates the Resistor Tolerance and the 6^{th} band color indicates the Temperature Coefficient of the Resistor.

*The Temperature Coefficient of the Resistor is the rate at which the Resistance of the Resistor varies with changes in Temperature. *

**Example:**

Qn:

*Given a six color band resistor with the color code Green, Blue, Black, Red, Gold and Orange as shown in the image above. What is the Resistor Value?*

* *Solution:

Consider the table below for a 6 band color Resistor:

For the first three bands, we find the color’s corresponding digit value. The given Resistor has **Green**, **Blue** and Black to begin with – which have digits 5, 6 and 0 ie (560). The forth band is **Red** which indicates that 560 should be multiplied by 100 that is 560 times 100 is 56000 or **56kΩ. **The fifth band is **Gold** which indicates a tolerance of +/- 5% and the Sixth band is **Orange** which indicates the Temperature coefficient of 15ppm/k.

**Therefore; The resistor value of the given resistor in question is 56kΩ with a tolerance of +/_ 5% and a Temperature coefficient of 15ppm/k.**

In case you are trying to memorize the resistor color codes simply use this mnemonic:

*“Bad Boys Rape Our Young Girls But Violet Gives Willingly”*

Alternatively, if you remember colors of the rainbow ie (ROYGBIV), simply remove “I” for Indigo then add Black and Brown to the front and Gray plus White at the end of the classical rainbow color-order. This gives us (BBROYGBVGW), the color codes for the Resistor.

**Decoding Surface-Mount Resistors:**

SMD resistors are small in size, and because of that there is often no room for the traditional color band code to be printed on them and as a result, new resistor SMD codes were developed. The most common codes are the three & four digit system and the EIA-96 system.

**The 3 & 4 Digit System:**

For this system, the first two or three digits indicate the numerical resistance value of the resistor and the last digit indicates the multiplier i.e the power of ten by which to multiply the given resistor value.

For-example here are some of the values under this system.

*340 = 34Ω x 10 ^{0} = 34Ω*

*243 = 24Ω x 10 ^{3} = 24,000 (24kΩ)*

*4782 = 478Ω x 10 ^{2} = 47800 (47.8kΩ)*

*0R6 = 0.6Ω*

*N.B: For Resistance values less than 10 ohms, we use the letter “R” to indicate the position of a decimal point. Thus 0R04 would be 0.04Ω.*

* *

**The EIA-96 System:**

The decreasing size of resistors combined with the high precision resistors created the need to have a new compact marking for SMD resistors and therefore the EIA-96 marking system was created. This was based on the E96-series aimed at resistors with 1% tolerance.

For this system, the markings exists out of three characters i.e two numbers and one letter eg “01A”. The two numbers in this case represent a code that indicates the resistance value with three significant digits and the letter is the multiplying factor that gives the final value of the resistor. For us to be able to decode this marking system, we shall use a tables below that show the values for each code which are basically the values from the E96 series. For-example the code 05 means 110Ω, code 33 means 215Ω as seen below:

**SMD marking system Table:**

**SMD Multiplier table:**

Qn:**Example:**

What is the Resistance value of the following SMD resistors?

(a). 04A, (b).38C, (c). 92Z

**Solution:**

From the tables above we see that the corresponding codes for 04, 38 and 92 are 107, 243 and 887. Then the corresponding multipliers for A, C & Z are 1, 100 & 0.001 respectively. Therefore we have:

*a).**.04A = (107 x 1) = 107Ω +/-1%*

**b).** .38C = (243 x 100) = 24.3kΩ +/-1%

**c). ** .92Z = (887 x 0.001) = 0.887Ω +/-1%

Note: The usage of letters prevents the confusion with other marking systems and one should also pay attention because the letter “R” is used in both systems. For resistors with tolerance other than 1%, different letter tables exists. It is always important to verify the manufacturers marking system.

**Resistor Power Rating:**

The power rating of a resistor is often hidden but it can be important when selecting a resistor type. Every resistor has a maximum power rating and it’s important to make sure the power rating is kept under maximum rating in order to keep the resistor form heating up too much.

Power is the rate at which energy is transformed into something else and it’s calculated by multiplying the voltage difference across two points by the current across them(ie P = VI).It’s measured in watts (W). Eg a resistor turns electrical energy running through it into heat energy. If we apply ohm’s law, we can also use the resistance value in calculating power and if we know the current running through a resistor, we can calculate power as:(P = Ior if we know the voltage across a resistor, then power can be calculated as:^{2}x R)(P = V^{2}/ R).

A resistor’s power rating is usually somewhere between 1/8W (0.125W) and 1W. Resistors with a power rating greater than 1W are often referred to as *“Power Resistors” *and they are used specifically for their power dissipating abilities. They can handle a lot more power before they blow up, small power resistors are often used to sense current.

**Resistors in Series & Parallel:**

Often times in electronics, resistors are paired together usually in series or parallel circuits and when combined, they create a total Resistance.

**Resistors in Series:**

Consider the illustration below,

When we connect *N* resistors in series as shown above, the **Total Resistance** is simply the summation of all the Resistor values. Let’s try and put it in an equation format for better understanding.

**R _{(total)} = R_{1} + R_{2} + ….. + R_{(N-1)} + R_{N} …………………………. (i)**

For-example if we need to have a 45.5kΩ resistor in our circuit, we could just simply connect a 45kΩ resistor and a 500Ω resistor in series to obtain the required resistance.

**Resistors in Parallel:**

Consider the illustration below:

To be able to find the Resistance of resistors in parallel is not as easy as we’ve just seen for the case of the series connection. For this case, we therefore say that, the total resistance of *N* Resistors in parallel is the inverse of the sum of all inverse resistances. Let’s try to re-write this statement in an equation format, perhaps it’ll make more sense that way.

**1/R _{(total)} = 1/R_{1} + 1/R_{2} + ….. + 1/R_{(N-1)} + 1/R_{N} …………………………. (ii)**

Note: The Inverse of Resistance is actually called Conductance i.e. the Conductance of parallel resistors is the sum of each of their conductances.

**Two Resistors in Parallel:**

If we only have two Resistors R1 and R2 in parallel, we can represent them with their parallel operator as R1 || R2 and their total resistance can be calculated with a slightly less inverted equation as shown below:

**R _{(total)} = (R_{1} x R_{2} ) / (R_{1} + R_{2} ) …………………………. (iii)**

If both of these two resistors in parallel have an equal value, then the total resistance is half of their value. For-example if we have two 50kΩ resistors in parallel, then their total Resistance is 25kΩ.

**Applications of Resistors:**

**Pull-up & Pull-down Resistors.**

In electronic logic gates, a Pull-up resistor is a resistor used to ensure a known state for a signal. Often times, pull-up resistors are used in combination with components such as switches and transistors which physically interrupt the connection of subsequent components to ground. It also ensure ensures a well-defined voltage across the logic gate during interruption. Consider the circuit below;

……………….

In the circuit above, when the switch is open, the voltage of the gate input is pulled up to the level of Vin and when the switch is closed, the input voltage at the gate goes to ground.

A pull-down resistor works in the same way but is connected to ground. It holds the logic signals at a low logic level when no other active device is connected.

**Voltage Dividers.**

In Electronics, a voltage divider is a passive linear (resistor) circuit that produces an output voltage (Vout) which is a fraction of its input voltage (Vin) and this is as a result of distributing the input voltage among the components of the divider.

The simplest example of a voltage divider is having two resistors connected in series with the input voltage applied across the resistor pair and the output voltage emerging from the connection between them as shown in the figure below;

The figure above shows a simple resistive voltage divider, the voltage from Vout to ground can be calculated as:

_{V(out)} = V_{(in)} x {(R_{2} ) / (R_{1} + R_{2} )} …………………………. (iv)

For-example if we have R_{1} as 2kΩ and R_{2} as 3kΩ with an input voltage Vin of 5V, then our output voltage Vout will be 3V.

**LED Current Limiting.**

Resistors are vital in protecting LEDs from blowing up when power is applied in a circuit. If we connect a current-limiting-resistor in series with an LED, the current flowing through these two components can be limited to a safe value. To determine the resistor value required in this case, we use Ohm’s Law as seen in the previous chapter. Therefore we need to know the forward voltage V_{f }required to make the LED light up and the maximum forward current I_{f .}

For-example in the circuit below, we have a 5V battery to power a red LED with a forward voltage of about 1.6V and a maximum forward current of 10mA. What is the value of the current-limiting resistor required?

**Solution:**

To calculate the value of the Resistor, we use the equation:

**R = (V _{s} – V_{f} ) / (I_{f} ) …………………………. (v)**

Where V_{s} = Source voltage (Power supply), V_{f } and I_{f } are the LEDs forward voltage and the desired current that runs through it respectively.

Upon entering the values in the above equation, we have R as:

**R = (5 – 1.6) / (0.01) = 340Ω**

**Conclusion:**

In this chapter we’ve covered the basics of everything resistors. That is decoding the color codes and the numbering system of through-hole and SMD resistors respectively and the simple applications of resistors in our circuits. By now we know that Resistors play a key role on any electric circuit out there and we should also know that resistors are not the only basic components used in electronics. In the next chapter we’re going to have a look at Capacitors.