# Ohm's Law, Resistors, and LED's

Current, Voltage, and Resistance are three properties of electrical circuits that allow us to specify parts, calculate needed values for various elements, and model circuits.

Let’s consider the example of water flowing through pipes, see the image below that was generated by baliscientist.com. We have a reservoir of water connected to a pipe. Voltage can be thought of as the pressure of the water preparing to flow through the pipes. Resistors can be thought of as the narrowing of a pipe that restricts the flow of water, where the flow of water is the electrical current.

Resistors are placed in series, or in-line in a circuit, with LED’s to protect the LED from burning out, because too much current through the circuit will eventually heat up and melt the inside of the LED’s. The typical preferred current through a 5mm LED is about 25mA. You can always put more current into an LED to increase brightness, but you will increase the risk of burn out. Different LED’s, and different colors of LED’s require different levels of current protection due to the different resistances across each LED, and thus require different resistors to protect them. The LED internal resistance results in a drop of voltage across the LED. The actual voltage in the circuit at the LED will be the difference between the supply voltage (VS) and the voltage drop of the LED (Vled) which you can see in the table further down the page.

**V = Vsupply – Vled**

The ideal resistance values are calculated using the mathematical relation between voltage (V), current (I), and resistance (R) called Ohm’s Law, seen below.

**V = IR**

The first step is to find our voltage value. Suppose we are using a USB port which provides 5V, and if we are using a red LED we will have a voltage drop of about 1.8V.

**Vredled = 5V – 1.8V = 3.2V**

The ideal current value across our LED is about 25mA. Substituting our voltage of 3.2V and our ideal current of 25mA into Ohm’s Law, we can solve for the resistor we need in our circuit.

**V = IR**

**3.2V = (25mA)R**

**R = 3.2V/25mA**

**R = 128Ω**

According to Ohm’s law, our ideal resistance would be 128Ω, however resistors tend to come in standardized values. The most common standard values of resistors are 10Ω, 12Ω, 15Ω, 18Ω, 22Ω, 27Ω, 33Ω, 39Ω, 47Ω, 51Ω, 56Ω, 68Ω, 75Ω, and 82Ω and all of these values’ multiples of ten, We need to pick the closest standard resistor value to the one we calculated, which would be 150Ω. In the table below the remainder of the standard resistor values recommended for each color LED have been calculated for you using the same process.

Now we need to learn how to determine what the resistance of each resistor is. The resistance value, measured in Ohms (Ω), is coded on each resistor using four or five colored bands. The chart below, courtesy of DigiKey, shows how to read the color code. Note that most resistors you will come across in hobby applications will have tolerances of 5% to 10%.

For example, a red LED needs a resistor with a resistance of 150Ω, which would have a four-band code of brown – green – brown – gold. If the resistor uses a five-band code, the bands would be brown – green – black – black – gold.

To help remember the resistor code, several mnemonics have been created that are easy to remember, such as:

**Big Brown Rabbits Often Yield Great Big Vocal Groans When Gingerly Slapped Needlessly**

**Better Be Right Or You’re Gonna Be Violently Gouged With Golden Spaghetti**

Once we choose which color LED we want to use, and which resistor we will use along with it, we need to understand how to place the LED in our circuit. LED stands for “Light Emitting Diode” and functions in a circuit to emit light, but also ensures that current only flows in one direction; think of them as one-way valves in our flowing water analogy. The nature of diodes, one-way flow, means their orientation in the circuit matters, we call this polarized. To help us distinguish which way the LED should be oriented one of the leads is longer than the other. The anode is the positive lead and is the longer of the two. The shorter lead is the cathode and is negative. See the diagram below courtesty of allaboutcircuits.com.