Labsson 2: Resistors, Variable Resistors AKA Potentiometers, and Resistor Ratings - madibabaiasl/mechatronics-course-v1 GitHub Wiki

In the previous lesson, we learned that the essence of electricity lies in the movement of electrons, which are responsible for the flow of electric charge in conductive materials. This flow, as we learned, is what constitutes electricity. In conductors, electrons move freely, enabling the efficient transfer of energy as electrical current. In contrast, insulators, with electrons tightly bound to their atoms, resist this flow, making them crucial in preventing unwanted current in electrical systems.

Now, let's think back to the class activity on the conductivity of water and saltwater. We observed that pure water, being a poor conductor, had higher resistance compared to saltwater, which showed lower resistance due to the ionization of salt. We also explored how electricity can be measured in terms of current (amperes) and voltage (volts). We delved into Ohm's Law, connecting these measurements with resistance. Just as we discussed batteries and their varying capacities and voltages, today, we will focus on a key component in controlling and managing these electrical properties in circuits - resistors.

Understanding resistors and their variable counterparts is crucial in designing and implementing efficient electrical circuits and thus mechatronics systems. As we proceed, we will explore:

• The various types of resistors and their functions in circuits.
• How to read resistor values and understand their importance in circuit design.
• The role of variable resistors and how they differ from their fixed counterparts.
• The crucial factors to consider when selecting resistors for different applications. ;

Before we dive into the details, let's do a quick activity to study the effect of resistors on the flow of electricity (current) in a simple circuit.

• First go to https://www.tinkercad.com/ and sign up and open up circuit simulation.
• Design a very simple circuit using a breadboard, a fixed resistor, a red LED, and a power supply (3.5 points). The electrical current should go through the resistor, then through the LED, and finally go back to the power supply. For now, take the value of the resistor to be $1K\Omega$ and the power supply should supply 5 V to the circuit. Notice the light of the LED. Calculate the current by hand using Ohm's law (suppose that the red LED drops 1.89 V) and verify it with the current that the power supply shows (3.5 points).

Start of the note about breadboards

For most breadboards, the layout and connection points are standardized to facilitate easy assembly and modification of circuits. The central area of the breadboard consists of rows of holes, divided into two sections by a central notch. Each row is typically a series of five connected holes, isolated from adjacent rows. These are called terminal strips and the connections are like this:

To insert a component into the terminal strips of a breadboard, gently push its leads into the holes of the terminal strip, ensuring each lead goes into a separate row to avoid short-circuiting.

On either side of the terminal strips are usually one or two columns of holes, running the length of the breadboard. These are known as bus strips. They are typically used for power connections – one row for the positive supply and one for the ground (or negative) supply. Components and rows on the terminal strip are then connected to these power lines as needed. The connections are like this:

End of the note about breadboards

• Now change the resistor to $10K\Omega$ and notice the difference in LED's light. Calculate the current and compare it to the one shown on the power supply. What do you conclude? Note: This time, the LED will drop about 1.77 V (3.5 points).

• Play around with different values of the resistor. What happens when the value of the resistor is too low say $1\Omega$? With a multimeter, measure how much voltage will be dropped on the diode this time? (3.5 points)

Make sure to take screenshots/photos and write notes as they will be helpful for writing the lab report.

Pencil lead, being made of graphite, a form of carbon, is an excellent material to create a makeshift resistor. Actually, carbon is the material that most resistors that we are familiar with are made of. A typical fixed resistor can be seen in the following figure:

Carbon is also used in the structure of variable resistors known as potentiometers.

• Get your pencil and create a strip of carbon with pencil lead drawn back and forth. This will create a resistive path using the graphite from the pencil, which acts as a form of variable resistor (3.5 points).
• Now get your multimeter and put it in the Ohm setting. Measure the resistance of this strip at different points along it. What is your observation (3.5 points)?

As we saw in the warm-up activities above, a resistor is an essential component in an electrical circuit that restricts the flow of electricity, thereby controlling and managing the current. This ability to modulate current is crucial for protecting sensitive components like LEDs and ensuring the circuit functions as intended. With this understanding, we can now delve deeper into the specifics of resistors, their types, applications, and selection criteria in this lesson.

Fixed resistors are marked with colored bands that indicate their resistance value and tolerance. The color codes can be extracted from the Color Code Chart below:

https://neurophysics.ucsd.edu/courses/physics_120/resistorcharts.pdf

Here's a guide to understanding the color coding system for 3, 4, and 5 band resistors.

These are the simplest type, typically found in older or less precise applications. To read their value follow these steps:

• The first two bands indicate the first two digits of the resistance value.
• The third band (multiplier) indicates the power of 10 which is the number that the two digits should be multiplied.
• They have ±20% tolerance

Class Activity: Find the resistance value of the following resistor. Express this value as a range based on the resistor's tolerance (3.5 points).

These are more common and include a tolerance band. To read their value, you can follow the following steps:

• The first two bands represent the first two digits of the resistance value.
• The third band (multiplier) functions the same as in 3-band resistors.
• The fourth band (tolerance) indicates the tolerance of the resistor, which is the range within which the actual resistance value may vary. Gold (±5%) and Silver (±10%) are common tolerance colors.

Class Activity: Find the resistance value of the following resistor. Express this value as a range based on the resistor's tolerance (3.5 points).

These offer higher precision with an additional digit for resistance value. This is how you can read their values:

• The first three bands indicate the first three digits of the resistance value.
• The fourth band (multiplier) functions like the third band in 3 and 4-band resistors.
• The fifth band (tolerance) is the same as the fourth band in 4-band resistors, providing the tolerance value. The tolerance band here can be any of the eligible colors and not just gold or silver. For example, if the fifth band is brown, then the actual resistance is within ±1% of the value. You can extract the tolerance value for different colors from the color code chart below:

https://www.codrey.com/tools/resistor-color-code-calculator/

In 5-Band Resistors, you maybe confused about which end to read the value because the 5th band can be any color. There is no straightforward way to solve this but you can look at the manufacturer's information or even better measure it using your multimeter.

Class Activity: Find the resistance value of the following resistor. Express this value as a range based on the resistor's tolerance (3.5 points).

Note that a schematic drawing for a fixed resistor is as follows:

Resistors can be connected in a circuit in two ways: in series or in parallel. Each configuration has its own characteristics and rules for calculating the total resistance.

In a series circuit, resistors are connected end-to-end, so the same current flows through each resistor.

The total resistance in a series circuit is the sum of all individual resistances. If you have resistors $R_1, R_2, R_3, ..., R_n$ connected in series, the total resistance ($R_{total}$) is given by:

$R_{total} = R_1 + R_2 + R_3 + ... + R_n$

The voltage drop across each resistor in series is different and depends on its resistance. According to Ohm's Law, V = RI, where V is voltage, I is current, and R is resistance. The same current flows through each resistor in a series circuit.

Class Activity: Series resistors

• Simulate two resistors of the values of $1k\Omega$ and $2k\Omega$ in series in Tinkercad and read the resulting resistance using a multimeter (3.5 points).

• Connect the resistors to a power supply of 5 V and calculate and verify the voltage drop by each resistor. What do you observe? Make sure to prove mathematically what you see on the multimeter (3.5 points).

Class Activity: Voltage Divider (3.5 points)

Consider the following circuit:

The power source supplies 15 v but we want the max voltage going to the computer to be 3.3 v. This means we should drop 3.3 v across the second resistor and consequently 11.7 v across the first resistor. Suppose we choose a nice high resistor (10k) for the second resistor. Based on these information, design the value of the first resistor so that you can supply 3.3 v to the computer.

Note: This circuit is called a voltage divider where we divided the incoming voltage into usable pieces.

In a parallel circuit, resistors are connected across the same two points, and each resistor has the same voltage across it ($V_{source} = V_1 = V_2 = .... = V_n$).

The total resistance in a parallel circuit is found by taking the reciprocal of the sum of the reciprocals of each individual resistance. For resistors $R_1, R_2, R_3, ..., R_n$ in parallel, it is given by:

$\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ... + \frac{1}{R_n}$

The total current entering the parallel combination (total current drawn) is equal to the sum of the currents through each resistor (drawn by each resistor) ($I_{total} = I_1 + I_2 + .... + I_n$). Ohm's Law applies to each resistor individually.

Class Activity: Parallel resistors

• Simulate (3.5 points) two resistors of the values of $1k\Omega$ and $2k\Omega$ in parallel in Tinkercad and read the resulting resistance using a multimeter (show this by calculation (3.5 points) as well).

• Connect the resistors to a power supply of 5 V and calculate and verify (using a multimeter) the current passing through the combination of two resistors (3.5 points). Now calculate and verify using a multimeter the current passing through each resistor. What do you observe (4 points)?

Note about measuring the current using the multimeter

To measure the current, you need to connect the multimeter in series with the circuit component. This means you have to open the circuit and insert the multimeter such that the current flows through the multimeter.

Important Notes for Real Multimeters:

• Be aware of the current rating of the circuit and ensure your multimeter can handle it. Exceeding the current rating of the multimeter can lead to blowing a fuse or damaging the multimeter. If unsure about the current, start with the highest current setting and then move to lower settings as needed.
• Never try to measure current directly across a power source like a battery or a power supply; this will create a direct short and could damage the multimeter or cause injury.
• Always turn off the multimeter after use to conserve battery life and prevent accidental damage to the multimeter or the circuit you're testing.

End of the note about measuring the current using the multimeter

• Suppose you need a $1k\Omega$ resistor but you have two $2k\Omega$ resistors. What would you do (2 points)?

Resistors come with various ratings that determine their suitability for different applications. Here are the primary ratings to consider:

1. Resistance Value and Tolerance. As we saw this at the start of this Labsson, the resistance value is measured in ohms ($\Omega$), and it indicates the amount of resistance a resistor provides to the flow of current, and the tolerance is expressed as a percentage (e.g., ±1%, ±5%) which indicates how much the actual resistance can vary from the stated value. A smaller tolerance means more precision.

2. Power Rating. Measured in watts (W), it specifies the maximum power the resistor can dissipate without damage. Common values are 1/8W, 1/4W, 1/2W, 1W, etc. Using a resistor with an insufficient power rating can lead to overheating and failure. Resistors directly convert the power they drop into heat so they need to be big enough to dissipate the heat without burning up. 1/4W resistors are the most common resistors and the resistors in our kit are of this type.

Example: Suppose we have a 10 ohm resistor and we run 200 mA through it.

The voltage drop across the resistor will be 2 V. Neither of the voltage or current is high, but let's calculate the power:

$P = VI = 2V\times 0.2A = 0.4 W$

This power is larger than the 0.25 W rating which will lead to burning out the 1/4 W resistor.

Note: The wattage rating of a resistor determines its size; higher wattage resistors are larger to provide more surface area for efficient heat dissipation.

Photo credit: www.electronicshub.org

3. Temperature Coefficient. This rating indicates how much the resistance value changes with temperature, usually expressed in parts per million per degree Celsius (ppm/°C). A lower coefficient is preferable for applications requiring stable resistance across temperature variations. Parts per million here refers to very small change in resistance relative to the resistor's total resistance. As an example, if you have a 1,000-ohm resistor with a temperature coefficient of 25 ppm/°C, and the temperature increases by 1°C, the resistance would change by 0.025 ohms (25 parts per million of 1,000 ohms).

4. Voltage Rating. It specifies the maximum voltage that can be applied across the resistor without causing breakdown or damage. This is often related to the physical size of the resistor, as larger resistors can handle higher voltages.

Class Activity: Finding resistor ratings

Choose a resistor from the list below and read and explain its ratings (3.5 points):

https://www.digikey.com/en/products/filter/through-hole-resistors/53

The power supply works by first stepping down the input AC voltage to a lower level suitable for the system using a transformer. After this, the rectifier converts alternating current (AC) to direct current (DC). It typically employs diodes to allow current to pass in one direction only, turning AC into pulsating DC. After rectification, the pulsating DC is still not smooth. A filter capacitor is used to smooth out these pulses to produce a more stable DC output. After this, a voltage regulator ensures a stable and consistent output. The regulator adjusts the voltage to the desired level and maintains it. This compensates for fluctuations in input voltage or changes in load.

The power supply that we have can operate on either 110V or 220V input voltages that cater to different regional power standards (please pay attention that before using it choose the proper standard - choosing 220 here in the US can damage your power supply but not choosing 110 in Europe where the standard is 220 V). It has an adjustable output voltage range of 0-48 V DC that is suitable for loads requiring voltage in this range. The current specification is at maximum 10 A. It's important to note that the current output is dependent on the load (device) and is not adjustable. This maximum current specification is suitable for devices needing up to 10A.

If you open this power supply, you can find the components below:

The large yellow component, with a metal core surrounded by coils of wire is the transformer that steps down the input voltage to a lower level. Rectifier is not very visible but typically includes a series of diodes; it should be on the circuit board, likely near the transformer, to convert AC to DC. The large cylindrical black components are filter capacitors that smooth out the DC current after rectification. The green board is the control circuitry that manages the output and protection features.

So, with the above explanation about our current power supply, we can see the important factors on choosing the right power supply for our application. The key factors to consider when selecting a power supply are voltage and current:

• Ensure the power supply can provide the correct voltage levels required by your components (motors, sensors, microcontrollers, etc.).
• Choose a power supply that can handle the maximum current draw of your system. Consider the peak current requirements, not just the average, to avoid overloading the power supply.

Variable resistors are components whose resistance can be adjusted within a certain range. You built one yourself in the warm-up activity. The most common type is the potentiometer, often referred to simply as a "pot." Potentiometers find applications in controlling electrical devices where adjustments of current or voltage are needed.

A potentiometer consists of a resistive element, typically a carbon or metal film, and a movable wiper. The wiper slides over the resistive element, changing the effective resistance.

The schematic diagram of a potentiometer is:

As the wiper moves along the resistive material, it varies the resistance between the wiper and each end of the resistor. This allows control over the current flow or voltage output.

For example if the wiper is in this position:

Then the resistance between the middle pin and the left pin is lower than the resistance between the middle pin and the right pin because you guessed it right there is less resistive material. The resistance between two outer pins is the max resistance and it is equal to the value of the pot.

In linear Potentiometers, the resistance changes linearly with the movement of the wiper, and logarithmic Potentiometers change resistance logarithmically, often used in audio for volume control as the human ear perceives sound logarithmically. For example, if you have a 10kΩ linear potentiometer and the wiper is at the midway point, the resistance from one terminal to the wiper and from the wiper to the other terminal is 5kΩ each. Ohm's Law (V = IR) is still valid here.

The wiring digram for a Pot can be depicted as the figure below:

Class activity: Exploring Potentiometer Behavior

• Get a known potentiometer and first measure the resistance between the outer terminals. How much is it and why (3.5 points)?
• Now turn the wiper half way and measure the resistance between the middle terminal and each of the outer terminals. How much is it and why (3.5 points)?

Class activity: Control the brightness of an LED using a pot

• Use an LED, a 1kΩ potentiometer, a power supply (set it to 4 V), and connecting wires to make an LED dimmer. Connect the potentiometer in series with an LED. Apply 4 V voltage to the circuit. Adjust the potentiometer and observe the change in LED brightness. Here is the schematics of the circuit (3.5 points):

Note that in practice, we also use another fixed resistor to protect the LED from over current but for the sake of this activity, we used just a potentiometer.

• Replace the pot with your handmade variable resistor (or pencil lead directly), and see if it also works (3.5 points).

• The grading criteria are as follows:

  • each activity and question according to respective points mentioned throughout the text (total = 90 points)
  • a conclusion paragraph that talks about what challenges you had and how you solved those (5 points)
  • references (disclose the use of AI) (5 points)

• Some useful notes:

  • Keep it concise and to the point.
  • You can use any text editing software that you are comfortable with, like Google Docs or Latex.
  • make sure to provide photos of the activities done when needed
  • include the labsson title and your name in the report