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Sadly, it is often that basic math concepts such as exponents, pi, and trig functions are not well explained in schools and therefore not understood by students. This often causes subjects such as mechanical or electrical engineering to seem out of reach.

I aim to create a website to help people of all ages to have a better understanding of, and get excited about these basic math concepts, and, for more advanced users who are interested, electrical engineering. The website would rely heavily on visual aids to help learning and have simple projects that would appeal to all ages. Projects for electronics would include “no-solder” instructions so that everyone could get started.

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The audience for this website would be those who want a better understanding of certain math subjects or concepts which I will cover. They will likely be people who are either interested in math, but don’t quite fully get one of these subjects, or people who are curious about these subjects and want a better understanding of them. They could also be those who are interested in fields such as Mechanical design or Electrical engineering but feel that the field is out of their reach due to their lack of understanding of mathematics. They could also simply be those who are looking to start Electrical engineering as a hobby and looking for some simple projects to get started.

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Electronic Basics: Ohm's Law

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Understanding it Better

There are many math concepts that are not always fully explained. Sometimes we are taught what they do but not what they are. Time doesn't always permit for teaching a better, more complete understanding, and we have to be satisfied with teaching just enough so that students can to use them.

Teaching just a basic understanding, while a useful strategy to cover a large scope of material, can lead to confusion and greater difficulty when attempting to apply these math skills and concepts beyond a basic problem. It is like having just a set of instructions on how to get to a destination. "Turn left here," "drive straight to there," "make a right at the next intersection"; these may get you to your destination most of the time, but what happens when there's a detour? Better than knowing just how to get there, is to know where you are going. A more complete understanding, one that extends beyond just the basic steps of how to do something, gives us a map of how concepts work together and how to apply them to a wider range of problems.

This site helps to bridge the gap between a basic understanding on how to do something and having a better perspective on how it works.

Having a Reason to Learn

It is hard to be motivated to learn something you'll never need. Many students take no interest in math because they don't use it in their everyday activities, or see how it applies to the world around them. Sometimes it seems they have math studies for the sake of having math studies.

This site offers a solution to this problem by showing how math applies to basic electronics problems and projects. By offering easy, no soldering actives that anyone can do, students can be motivated to take greater interest in their math studies.

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Pi[Page 2]

Pi

Pi is great! It can even be used to describe the dimension of actual Pie (the one everybody actually likes). It's uses are many, and when you have a better understanding of what it is, you can better appreciate it and it's uses in the world around us.

But What is Pi?

When asked, most people know that Pi is a number that is approximately 3.14, and that on or around March 14^th teachers bring pie to school to try and make math class more exciting. But have you ever stopped to ask yourself why? Why is it approximately 3.14? Why is it important? What does it mean? You may have an idea of the "value" of Pi, but what is it?

Before we begin...

Pi has a lot to do with the geometry of circles, so just to be sure we're all on the same page, it's important to know what these three of the basic items are: Circumference, Diameter, and Radius. Don't worry though, these are actually very simple.

Circumference: The length of the outside or perimeter of a circle. This is usually written as 'C'.
Diameter: The length from one side to the other of a circle, though the center point. This usually written as d.
Radius: The length from the center of a circle to its side. The radius is usually written as 'r'.

What Pi is

Pi is the ratio of length of a circle's circumference compared to it's diameter. This may sound complicated, but the concept is actually quite simple. It just means if you were to cut a circle's perimeter and lay it flat next to the diameter, it would be 3.14 times longer than its diameter!

Great, but now what?

Now that you know this is a ratio that works for all circles you can use it to figure out all kinds of problems! But lets start with something a little simpler to better understand this concept, and that of ratios in general.

Two ropes

Imagine you have two ropes. You know one is twice as long as the other. You know the short one is 5ft long, so what is the length of the longer rope?

The solution to this problem is pretty simple. Since the long rope is two times the length of the short rope, and we know the length of the short rope, just multiply two times the length of the short rope to get the length of the long rope. Do this and you get that the longer rope is 10ft long.

We can apply the idea of the ropes to any circle to figure out it's circumference. The diameter is the short rope, and the circumference is the long rope. Instead of being two times longer, it's a little over three times longer (3.14 to be more precise). So now just multiply 3.14 times the length of the diameter and you will have the length of the circumference!

Neat Trick is an Equation...

Our little comparison to ropes is a nice way to get a better understanding of what Pi is, but it can be simply written as Pi times the diameter of a circle equals its circumference. That's right, it's actually an equation.

πd = C

Typically, this equation is written in terms of the radius. The radius is half the length of the diameter, so we can re-write the equation as Pi times two times the radius equals the circumference.

π2r = C

One last modification, whenever you have a mix of an actual number and symbols or variables multiplied together, it's convention to put the number first, followed by the symbols and variables. This number actually even gets a special name. It is called the coefficient. When we fix this last bit we get something that may look familiar to you:

2πr = C

In the shell of a nut...

In short, Pi is just a comparison between the length of the diameter and the circumference of a circle. With this understanding and the previous equation, you can now find the circumference of any circle with just the length of it's diameter or radius and vice versa!

This is just a touch of the power of Pi though. While using Pi to find a circle's circumference is a simple way to better understand what it is and where it comes from, it's uses and abilities stretch far beyond into various fields of study. It is also used for simple things like finding the area of a circle, to complex things like describing the shape of an involute gear, and to various things such as understanding and modeling alternating current.

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Exponents[Page 3]

What are Exponents?

Summary:

xⁿ = x * x * ...x (n times)

Exponents represent how many times a term (a variable or number) is multiplied by itself. For example:

x³
Is the same as:
x * x * x

Adding Variables With Exponents

Summary:

x^a + x^a + x^b + x^b = 2x^a + 2x^b
(Note: You can not add terms with different exponents.)

Just like with adding any other like terms you can "condense" terms with exponents, or represent adding the same thing multiple times though multiplication. For example:

x + x
Is the same as:
2x
and
x^a + x^a
Is the same as:
2x^a

We can see this is true if we were to substitute x for five:

5 + 5 = 10
Is the same as:
2(5) = 10
Just like:
5² + 5² = 25 + 25 = 50
is the same as:
5² + 5² = 2(5²) = 2(25) = 50

In order to combine terms the exponents of the terms must be the same. If you have multiple terms, some with the same exponents, and some not, then you can add the ones with the same exponents, but not the others. For example:

x² + 3x² + 2x² + 2x³ + x³ + 4x³ + x⁵ + 7x⁶
Is the same as:
6x² + 7x³ + x⁵ + 7x⁶

In the example above, 6x² + 7x³ + x⁵ + 7x⁶ is as reduced as the equation can be because we cannot add the terms with different exponents. While the terms may be the same, the numbers represented as a whole are very different when the exponents do not match.

This difference becomes obvious when you substitute in any number (barring zero or one) for the term. For example five raised to the second power (5² = 25) is very different from five raised to the third power (5³ = 125). If you attempt to combine these you soon find that the rules for doing so would be ambiguous. Which exponent would you use for the combined term? These problems become evident when trying to add 5's with different exponents:

5² + 5³ = 5² + 5³ = 5² + 5³
↓
5² + 5³ ≠ 2(5²) ≠ 2(5³)
↓
25 + 125 ≠ 2(25) ≠ 2(125)
↓
150 ≠ 50 ≠ 250

Product Rule (Multiplication)

Summary:

x^a * x^b = x^{a + b}

When multiplying same terms together, you can simply add the exponents. Remember, exponents are a way of telling you how many times you are multiplying a term by its self. You can think of this as the count of a "group". If you then multiply one group by another group of the same term, you are essentially just making the count of that "group" larger.

x² * x³ = x⁵
Is the same as:
(x * x) * (x * x * x) = x * x * x * x * x

We can see this example works if we replace x with 3:

3² * 3³ = 3⁵
↓
9 * 27 = 243
↓
243 = 243
Is the same as:
(3 * 3) * (3 * 3 * 3) = 3 * 3 * 3 * 3 * 3
↓
(9) * (9 * 3) = 9 * 9 * 3
↓
(9) * (27) = 81 * 3
↓
243 = 243

Quotient Rule (Division)

Summary:

x^a

x^b

= x^{a - b}

Similar to multiplication, division of like terms with exponents can be calculated by subtracting the divisor's exponent from the dividend's exponent. Remember that a number divided by itself is equal to one, and multiplying a number by one does nothing. Since when you are dividing two like terms with exponents, you are essentially dividing two "groups" of the same numbers, the terms in one group negate the effects or "cancel out" the terms in the other group.

x⁵

x³

= x^{5 - 3} = x²

Is the same as:

x * x * x * x * x

x * x * x

= 1 * 1 * 1 * x * x = x * x

Negative Exponents

Summary:

x^-a =

1

x^a

Negative exponents are actually the inverse "fraction" of the term to the absolute value of the exponent. That is in other words one divided by the term to the (non-negative) exponent.

x^-3 =

1

x³

=

1

x * x * x

We can see how this "inverse" is actually the same as a negative exponent when using the quotient rule.

x³

x⁵

= x^{3 - 5} = x^-2

Is the same as:

x * x * x

x * x * x * x * x

= 1 * 1 * 1 *

1

x * x

=

1

x * x

Power Rule

Summary:

(x^a)^b = x^{a * b}

When one term raised to an exponent is raised to another exponent, you multiply the exponents together. Remember that and exponent is essentially just saying, "A thing times its self this number of times". In the case of the exponent being outside the parenthesizes, the thing multiplied by itself is everything in the parenthesizes! This becomes evident when you write it out.

(x²)³ = x^{2 * 3} = x⁶
Is the same as:
(x²)³ = (x²) * (x²) * (x²) =
(x * x) * (x * x) * (x * x) =
x * x * x * x * x * x

Factors and Roots

Factors are sort of the "DNA" of numbers. They are the numbers when multiplied together make up a number. Any integer number can be divided into its factors. A number's factors can also be one and itself. For example the number 15's factors are 1 and 15, as well as 3 and 5. If a number's factors are only one and itself, then the number is a Prime Number.

Typically when finding the factors of a number we are trying to find its lowest, most broken down, or prime factors. For example the number 100 could be broken down into 4 and 25. While these are factors of 100, each can still be broken down into smaller numbers. 4 can be broken down into 2 and 2. 25 can be broken down into 5 and 5. We can combine these to get the full list of the prime factors of 100 as 2, 2, 5, and 5.

Factors of 100:

A Root is a specific factor, when multiplied by itself a number of times (depending on what "root" it is), creates the number. For example 2 is the Square Root of 4, as well as the Cubed Root of 8.

√4 = 2
2 * 2 = 4

∛8 = 2
2 * 2 * 2 = 8

The symbol to denote finding the root of a number is the Radical Symbol. The number outside or above the "v" part of the radical indicates the degree of the root (i.e. how many of the root are multiplied together to get the number inside the radical). If the radical is left "empty" then it is convention that it represents the Square Root (i.e. 2).

More Examples:
√4 = 2
2 * 2 = 4

∛8 = 2
2 * 2 * 2 = 8

∜16 = 2
2 * 2 * 2 * 2 = 16

√25 = 5
5 * 5 = 25

√9 = 3
3 * 3 = 9

∛343 = 7
7 * 7 * 7 = 343

∜6561 = 9
9 * 9 * 9 * 9 = 6561

You may have noticed in the last example above, 9, is not a prime factor of 6561. While a root is often a lowest factor, or a prime number, it does not have to be. The square root of 100 for example is 10. In fact, a root doesn't even have to be a whole number or can also be an irrational number, such as √2 (≈1.414).

More Examples:
√100 = 10
10 * 10 = 100

√625 = 25
25 * 25 = 625

∛3375 = 15
15 * 15 * 15 = 3375

√2 ≈ 1.4142
1.4142 * 1.4142 ≈ 2

∛5 ≈ 1.7099759
1.7099759 * 1.7099759 * 1.7099759 ≈ 5

Fractional Exponents, i.e. "Roots"

Fractional Exponents, i.e. "Roots"
x^a/b = z^a
where
z^b = x
i.e. z is the "b^th-root" of x

Fractional exponents may seem complicated, but the idea behind them is actually quite simple. Lets start by thinking of a number's roots as a part or "fraction" of that number's factors. Note that without multiplying all of the roots together we do not come out with the whole number.

Roots as a Fraction of a Whole Number:

We see that the cubed root of 27 is three. If we think of each root factor as a part of the whole, then when we have all of them multiplied together we get 27.

If we take away 1/3^rd of those root factors we are then only left with two of the three root factors, or 3 * 3 which is equal to 9.

1/3^rd of 27's cubed root factors is three.

Here we can begin to see how the fractional exponent correlates with the term's root factors. The denominator tells us the degree of the root it is dividing its term into. That is, it tells us how many root factors it is breaking the number into. The numerator tells us how many of those root factors we are keeping to multiply together.

With this in mind we can see how each fractional exponent relates to the first three root degrees.

First Three Root Degrees as Fractional Exponents:

√x = x^1/2,
because we are breaking x into two root factors and only keeping one.

∛x = x^1/3,
because we are breaking x into three root factors and only keeping one.

∜x = x^1/4,
because we are breaking x into four root factors and only keeping one.

While the denominator determines how many root factors we are breaking the number into, the numerator affects how many of them we "keep" to multiply together. It is essentially adding an exponent to the result of finding the root.

Root Equivalents of Fractional Exponents:

x^1/2 = (√x)¹,
because we are breaking x into two root factors and only keeping one.

x^2/3 = (∛x)²,
because we are breaking x into three root factors and keeping two.

x^3/4 = (∜x)³,
because we are breaking x into four root factors and keeping three.

x^3/2 = (√x)³,
because we are breaking x into two root factors but have three of them that size.

To write this relationship, lets define z as a root factor of x, which is of degree b. That is to say that z^b = x or that the b root of x is z. If we then raise x to a fractional exponent in the form of a/b, (x^a/b) we would get z^a.

Relationship of Roots and Fractional Exponents:

z = ^b√x, i.e. the b^th root of x

so that:
z^b = x

then:
x^a/b = z^a

We can further illustrate this relationship by showing the factors we "keep" out of the normal root factors:

Examples of Fractional Exponents:

16^3/4 = (∜16)³ = 8

16

↓

2

↓

2

*

*

↓

2

↓

2

*

*

↓

2

↓

2

*

= 8

↓

2

= 16

27^2/3 = (∛27)² = 9

27

↓

3

↓

3

*

*

↓

3

↓

3

*

= 9

↓

3

= 27

100^1/2 = (√100)¹ = 10

100

↓

10

↓

10

*

= 10

↓

10

= 100

15625^2/3 = (∛15625)² = 625

15625

↓

25

↓

25

*

*

↓

25

↓

25

*

= 625

↓

25

= 15625

27^3/3 = (∛27)³ = 27

27

↓

3

↓

3

*

*

↓

3

↓

3

*

*

↓

3

↓

3

= 27

= 27

823543^5/7 = (⁷√823543)⁵ = 16807

823543

↓

7

↓

7

*

*

↓

7

↓

7

*

*

↓

7

↓

7

*

*

↓

7

↓

7

*

*

↓

7

↓

7

*

= 16807

↓

7

*

↓

7

= 823543

16^5/4 = (∜16)⁵ = 32

16

2

*

↓

2

↓

2

*

*

↓

2

↓

2

*

*

↓

2

↓

2

*

*

↓

2

↓

2

= 16

= 32

Exponents of Zero

Summary:

x⁰ = 1

Any number raised to the zero^th power is one. This may seem odd since typically you think of zero of something as zero, but it becomes evident once you do out the math.

Division of exponents can be used to help us better understand this. When dividing two terms you subtract the exponents, canceling out some of the terms on both sides of the dividing line. Consider what is happening to cancel out these terms and why. They can't be reduced to zero because it would cause the remaining terms to be reduced down to zero as well when multiplied. The reason they cancel out is because you are dividing a number by itself, which is always one.

Division of Same Terms Cancel out:

x³

x²

= x^{3 - 2} = x¹

Is the same as:

x * x * x

x * x

= 1 * 1 * x = x

Now consider the case of when you have an equal number of terms on either side of the dividing line. All terms would "cancel" each other out. Each and every term would be reduced to one, and one multiplied or divided by any number of ones will remain one.

Division of Same Terms Cancel out:

x³

x³

= x^{3 - 3} = x⁰ = 1

Is the same as:

x * x * x

x * x * x

= 1 * 1 * 1 = 1

Exponents of One

Summary:

x¹ = x

Any term raised to an exponent of one is itself. This actually makes perfect sense as it is essentially saying you have one group of a number. It can also be shown mathematically as previously done for exponents of zero.

Division of Same Terms Cancel out:

x³

x²

= x^{3 - 2} = x¹

Is the same as:

x * x * x

x * x

= 1 * 1 * x = x

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Basic Electronics: Ohm's Law[Page 4]

What is Ohm's Law?

Ohm's law describes how Voltage, Current, and Resistance all relate to one another in a circuit. It was discovered and later published in 1827 by German physicist Georg Ohm. It is the base on which many other principles of electronics stand. It states that the voltage is equal to the current times the resistance. But what does this mean? What are voltage, current, or resistance?

A Little Analogy

Often to describe how a circuit works and Ohm's law, the circuit is compared to a water hose. This analogy, while not perfect, has many parallels and does a pretty good job on helping us understand the basic idea of Ohm's Law and how to use it.

Current

In electronics, electrons are used as the power source. An electron is a negatively charged particle. Just like a magnet's negative pole is attracted to another magnet's positive pole, electrons are negatively charged and attracted to positive charges. Electrons in the negative side of a power source are attracted to the positive side of the source. The differently charged sides of the source are connected by a circuit allowing electrons to flow though the circuit from the negative side to the positive side.

This flow of electrons is called the Current. The current, in our hose analogy, is compared to the water that flows though the hose. When we refer to current in Ohm's law, we are describing the rate at which electrons are flowing though the circuit.

This flow rate of the current is measured in Amperes (usually referred to as Amps). One amp is roughly equivalent to 6.24 × 10¹⁸ electrons per second.

NOTE:

While physically current flows from the negative side of a power source to the positive side, convention in electrical engineering treats current as though it flows from the positive to negative. While using either method will work as long as consistency is used, we will be following convention and treating current as though it flows from positive to negative. This may seem confusing at first, but just do your best to keep it in the back of your mind and not focus too much on the doublethink.

Resistance

Resistance is the force that restricts or pushes against the current. You can think of this like squeezing or putting your thumb over the end of the hose. When you do this you can feel the water pushing against the resistance you've created.

The unit used to measure resistance is called the Ohm.

Voltage

Voltage is the force that pushes the current though the circuit. It can be compared to the water pressure in our hose that pushes the water though the hose. If there is no voltage, no current flows, just like with no pressure, no water flows.

In order to create a voltage in a circuit, there needs to be some resistance. In a hose without resistance, the pressure inside remains at just about the same pressure as the outside of the hose, and all the water quickly flows out the end. If you were to squeeze the hose you could feel how little pressure there was pushing back.

When you restrict the flow of water at the end of the hose, flow decreases, but pressure can begin to build up.

The unit used to measure voltage is the Volt.

Using Ohm's Law

Now that we have a better understanding of how voltage, current, and resistance relate, we can start to see how to use Ohm's law:

Ohm's Law

Voltage (V) = Current (I) × Resistance (R)

Using this equation you can calculate any one of the variables using the other two. Try out the voltage calculator below to get a better feel for how this relationship works:

Ohm's Law Calculator

V = I × R

Voltage:
Current:
Resistance:

Use the text boxes to adjust the value of the either the voltage, current or resistance. The blue box ( ) shows which value is being calculated (either current or resistance). The size of the variables in the equation will reflect their values as you adjust them.

Ohm's law shows how to calculate the voltage in a circuit. Using some simple algebra you can alter the equation to calculate either the resistance or the current:

Equation for Current:

I =

Equation for Resistance:

R =

Moving Forward

With a better understanding of Ohm's Law you can start to get the basic idea of how a circuit works. The continued practice of using it will help to solidify its principles. This website has tutorials for practice that are accessible to beginners and include instructions that requires no soldering. Check it out and continue learning!

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Project: Making a Simple LED Circuit[Page 4]

What is an LED?

LED stands for Light Emitting Diode. A diode only allows current to flow though it in one direction. There is a wide range of diodes with a number of versatile functions and abilities. A Light Emitting Diode is one that also emits light when passing a current though it. Today they are quite common and can be found in items like the household lightbulb, or specialized items like traffic lights.

Turning it on

You can think of a diode sort of like a one way door for current. Pushing on one side will open it, but pushing from the other side wont. Unless of course you push really hard from the other side and you break it. This backwards breaking limit is called the Reverse Voltage Limit.

Also like our one way door, a diode requires a little push before it will open and allow current to pass though. This "little push" is called the Forward Voltage. This limit basically tells us at what voltage our circuit needs to be before the LED will turn on and open for the current to pass though. Below this there is still some "seepage" of current, but it is negligible and doesn't really need to be considered for our purposes.

You should be able to find the forward voltage limit in the documentation from your vender. Sometimes it can be with the product information but often it will be found on a document from the manufacturer called the data sheet or spec sheet. Sometimes, due to the inaccuracies of mass manufacturing, the forward voltage limit can be given as a range instead of a single set value. In this case you may need to make multiple calculations for how those upper and lower limits may affect your circuit.

The diode will resist any attempts to have its voltage increased beyond its forward voltage limit. Small increases in the voltage to the diode create drastic increases to the current that passes though. More current passing though the LED will make it brighter, but too much will burn it out! The current needs to be limited to prevent destroying the LED. This limit should also be provided by the vendor or on the data sheet from the manufacturer. It should be called the forward current or current limit.

//LED CURRENT DIAGRAM HERE

Limiting the Current

The simplest way to limit the current though the LED is with a resistor. We can use the relationship in Ohm's Law to figure out how many ohms our resister needs to be. We just need to replace the variables with our our own limits and values, then solve for the resistance.

Ohm's Law

V = I × R

Let’s start with the voltage. We don't use the entirety of the power supply’s voltage when calculating the value the resistor, just the amount that exceeds our forward voltage threshold. You can think of this current limiting resistor kind of like a weir. A weir is a sort of underwater damn that constricts only part of the water’s flow in order to control it. The amount of voltage we need to limit can be calculated simply by subtracting the forward voltage of the LED from the voltage of your power supply.

//PICTURE/DIAGRAM OF A WEIR

(Power_Supply_Votage - Forward_voltage) = I × R

Next add in the current we want to pass through our LED. You can figure this out from your forward Current or current limit. You won't want to use the exact given limit though, this is the threshold of what the LED can take before it starts to burn out. You will want to use a little less than this to create a little bit of a buffer as real world components can vary a little from the ideals of our calculations.

(power_supply_voltage - forward_voltage) = (forward_current - safety _buffer) × R

Now that we have all the information we know added into the equation, we just have to solve for the resistance. To do this we just need to divide both sides by the current.

(power_supply_voltage - forward_voltage)

(forward_current - safety_buffer)

= R

Now that we have the equation for the resistance, we just have to plug in our values and solve.

Tutorial

Materials

Before we begin, we will need to select and gather the different components needed to create the LED circuit. These include a power supply, the led(s), the resistors, wires, and something to connect them all together.

Wires/Connectors

Usually a circuit is soldered together using solder and a soldiering iron. This, however, can be dangerous and intimidating to beginners. Instead of solder, in this tutorial we will be using mostly female jumper wires as are easy to get and can be connected by simply plug a pin or wire directly into their connector. The jumper wires do restrict you to using a single strand or "solid core" wire (wire made of a single wire and not multiple strands) since it needs to be thin and rigid enough to be plugged into the connector.

You can make your own jumper cables using wire, Dupont Male and Female Connectors, and a Crimping Tool. You may even need to do this like I did for my own power supply, since its connecting wires were made from multiple strands.

Power Supply

I have selected a power supply that runs on two AA batteries. Each battery is 1.5 volts so the total voltage of the supply should be 3 volts. However, measuring the power supply we see that it is 3.18 volts! This is because I used two new AA batteries which are typically a little over 1.5 volts. You should always account for variances such as this and add in a buffer when making your calculations. I will consider it as a 3.3volt power supply, as future replacement batteries may vary even more.

LED

LEDs come in many different shapes and sizes. I have selected a red, through-hole LED to use. Through-hole simply means it has small pins or wires that are meant to be placed through and soldered to a hole in a circuit board. These will be useful for us since they can be plugged into our jumper wires to connect them without soldering.

From the manufacturer I can see that my LED needs between 1.9-2.1 volts for its forward voltage. In my calculations I will use the lower limit of 1.9 volts to be on the safe side. If you do not have the information for the forward voltage from the manufacturer, you can use the table below as a general rule of thumb for the forward voltage by LED color.

COLOR	TYPICAL VOLTAGE
RED	1.8v
ORANGE	2.0v
YELLOW	2.1v
GREEN	2.1v
BLUE	3.0v
WHITE	3.0v

We also need the forward current for our LED. The vendor of my LEDs posted that it is 20mA (0.02 Amps). If you can't find the forward current for your LED you can use 20mA as a general rule of thumb for through-hole LEDs. To be on the safe side I will use a safety buffer of 2mA for my calculations giving me a current of 18mA.

Resistor

Now that we have all of the values for our components, we can calculate the resistance we need for our resistor. First start with the equation to find the resistance:

R =

(power_supply_voltage - forward_voltage)

(forward_current - safety_buffer)

Next, fill in all of the information that we have:

R =

(3.3 - 1.9)

(0.02 - 0.002)

Now we just need to solve the equation to find the value we need for our resistor:

R =

(3.3 - 1.9)

(0.02 - 0.002)

⇓

R =

1.4

0.018

⇓

R = 77.7Ω

Selecting a Resistor

Usually resistors will come at different set levels and we won't find the exact resistance we need. You can get around this by adding different resistors in series, or one after another. When you do this the resistance adds up and acts like one resistor. So I could select a 75Ω resistor and a 3Ω resistor to get a 78Ω resistor.

My resistors jump from 75Ω to 100Ω. Since I used the worst case limits in my calculations I will simply use the 75Ω resistors as it will still likely be under the 20mA limit. In fact we can use Ohm's law to find what the current will be using the 75Ω resistors:

1.4

= 0.0186Amps or 18.6mA

We can see that 18.6mA is still under our current limit of 20mA, so we should be ok using the 75Ω resistor.

Assembly

Now that we have all our components, we can begin to assemble our LED circuit. As we are using jumper wires, the circuit goes together and can disassemble fairly easily. Unfortunately it can sometimes come apart when we don't want it to, so you may consider placing a small bit of tape on the junctions to help hold it together if you want to use it for something else.

First I will begin by attaching a female to female jumper cable to my resistor. It doesn't matter in the circuit which side of the LED that the resistor is on, but in my circuit I will be placing it in front of the positive side of the LED.

As I want to attach the resistor to the positive pin of the LED I need to identify which side is positive. The positive side of the LED is called the Anode. The negative side is called the Cathode. On a new LED you will notice that one pin is longer than the other. It is the convention that the anode is the longer pin and the cathode is the shorter one.

If you're not sure if your LED has been trimmed and you want another way to check, you can look close inside of it to find out. As it is clear to let light out, you can also look in to see what the anode and cathode attach to. You will notice one side is larger than the other. The smaller side is called the Post, and is usually shaped a bit like a chair or a nose. This is the anode.

The other side is called the Anvil and is shaped, well, a bit like an anvil with a cup in the top of it. This is the cathode. The cup on top is where the LED produces the light.

Now that we've identified the anode, we can plug it into the jumper cable attached to the resistor.

Next we can attach another cable to the other side of the resistor, as well as another cable to the other side of the LED. These cables will attach to the power supply, so depending on what kind of connector it has you may have to mix and match your jumper cables. My power supply uses a female connector, so I am using a male to female connector.

//img containing the led/resistor attached to mail/female cable and female power supply connector all in frame

A Note On Power Safety:

While the power levels we are working with are pretty safe (just a little over 3 volts for me), it is still important to practice good safety procedure. Even a single battery under the right conditions can be dangerous. There is even a survival technique to start a fire using a single battery and foiled gum wrapper.

The danger from these low voltages comes mainly from shorting the power supply, or connecting to the positive terminal directly to the negative terminal with little or no resistance in between. If you look again to Ohm's Law, you notice that with little or almost no resistance, our current becomes huge. That much current tends to heat things up fast! Not only is this not good for the power supply, but it can lead to burns or even start a fire under the right conditions.

Make sure to follow these safety procedures:

If your power supply has a switch, make sure it is in the OFF position.
If your power supply has batteries, make sure they are removed until the circuit is complete.
If you power supply runs on wall power, make sure it is unplugged until the circuit is complete.

Final assembly

We can now attach the jumper cables to the power supply. Since I attached my resistor to the anode of my LED, I will plug that wire into the positive terminal of the power supply, and the other wire to the negative terminal. If you are unsure which is which on your power supply, you can usually identify them by the wire colors. Red Wires are usually used for the positive terminal. Black Wires are usually used for the negative terminal.

Now that the circuit is assembled we can install our batteries and turn on the power supply. The LED should light up!

Trouble shooting

LED Does Not Light Up:

The LED may be backwards or attached to the terminals backwards.
- Try switching the wires attached to the LED.
Your batteries may be low or dead.
- If you have a battery checker, check their power levels to see if they are good.
- Try replacing them with new batteries.
The LED may be defective.
- If you have more than one LED, try switching it out for another one.
The Resistor may be too big.
- Check your calculations and that the values you have for your components are correct.
- Try using a slightly lower value for your resistor and see if it lights or even lights dimly.

LED Only Lights Dimly

Your batteries may be low.
- If you have a battery checker, check their power levels to see if they are good.
- Try replacing them with new batteries.
The Resistor may be too big.
- Check your calculations and that the values you have for your components are correct.
- Try using a slightly lower value for your resistor and see if it lights or even lights dimly.

LED Lights Brightly, then Dies, or Immediately Dies

Note: If your LED lights brightly and then stops, it has likely been burned out and is dead. You will need to replace it with another one.

The Resistor may be too small.
- Check your calculations and that the values you have for your components are correct.
- Try using a higher value for your resistor and see if it lights and does not burn out.

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