*The following information is a single lesson in a larger project. Find more great projects *here*.*

**Return to Previous Lesson: **Current, Resistance, and Voltage

**Lesson Overview:**

Now we'll learn about Ohm's law and how to use it!

## Step 1: Introduction

Current, voltage, and resistance are all related to each other in an electrical circuit. When you change one, you affect the others. The mathematical relationship between them is called Ohm's Law, named for Georg Simon Ohm, who discovered it.

Ohm's Law applies to a the voltage across, current though, and resistance of a single component (such as a resistor).

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

As you will see in the following steps, our main concern in this project is controlling current flow in the wires and components. Again, we will use the multimeter to measure voltage and current in the circuit.

__Instructions__

- The diagram above highlights the resistance of, voltage across, and current through a resistor in an LED circuit.
- Continue to the next step.

## Step 2: Ohm's Law

In the last lesson, you used multimeters and an LED to visualize these trends:

Higher resistance reduces current and reduces LED brightness

Higher voltage increases current and increases LED brightness

These trends are consistent with the equation for Ohm's Law!

You can rearrange Ohm's Law a few different ways using the triangle diagrams below as a guide. If you put your finger over the circled letter, you can see how the other two variables relate to each other.

- Examine the different forms of Ohm's Law, shown above. Do the equations support the trends that you observed?
- When voltage is constant, current and resistance are inversely proportional to each other.
- When resistance is constant, voltage and current are directly proportional.
- Continue to the next step.
- Stuck?
**HINT:**When current is held constant, a larger resistor will have a higher voltage over it. This might not seem relevant now - but we will use every form of Ohm's Law in future lessons!

## Step 3: Resistor Circuit

Remember, this project is all about what is happening inside the conductive materials in the circuit - the wires and the resistor. So to simplify things, we took away the LED.

The circuit diagram below matches the circuit in the Workplane. Current is running through the button and resistor. The resistor is the only load in the circuit, meaning that is the only component that uses energy from the battery.

You can't see anything happening when you press the button, but in real life the resistor would respond by heating up!

- In the diagram above, current is flowing in the direction of the red dotted line.
- This resistor circuit is already in the Workplane. There are no output components, so you won't see anything happen if you simulate the circuit! However, take a moment to visualize the flow of current through the breadboard circuit.
- Continue to the next step.
- Stuck?
**HINT:**Resistive heating is actually an effect used in some devices. A toaster is a good example. It contains a resistive "heating element" that gets very hot when current runs through it.

## Step 4: Setting Up an Experiment

In this step, we will add two multimeters to the circuit:

Measure current in the wires

Measure voltage across the resistor

We don't need a meter for the resistor -- you'll know the resistance by setting it yourself with the dropdown menu!

You can use what you learned about multimeters in the previous lesson to add these tools to the circuit. Detailed instructions are below.

- Drag two multimeters into the Workplane from the Components + menu. Arrange these next to the resistor and the top of the breadboard.
- Connect the first multimeter across the resistor component with wires. Use the dropdown menu to change its mode to "Voltage."
- Next create a break in the top red wire and complete the circuit using the multimeter, as in the picture below. Use the dropdown menu to change the mode to "Amperage."
- Finally, simulate the circuit and press the button! You should see a reading on both meters. The voltage reading will be approximately 9V (like the battery) and the current will be in the milliamp (mA) range.
- Continue to the next step

## Step 5: Ohm's Law Experiments

In this section, we'll ask you some questions about current and voltage levels in your circuit.

Refer to the diagrams below to perform some simple calculations, and use the simulator to check your results.

- In this step you'll keep the voltage constant (9V, set by the battery). Can you predict what the current in the circuit will be if you use the following resistor values? Use the equation I = V/R -250 ohms -500 ohms -750 ohms -1000 ohms (or 1 k-ohm) -2000 ohms (or 2 k-ohm) After you make your calculations, start the simulation! Hold the shift key and press the button to turn on the circuit. Change the resistor value to each value listed above and check your values of current.
- Next we will keep the value of the resistor constant and see what happens when you change voltage. Highlight the resistor and change its value to 300 ohms.
- With a resistance of 300 ohms, can you predict what the current will be if you change the voltage? - 9 volts - 3 volts - 1.5 volts After you make the calculations, start the simulation and press the button. You can change the voltage by swapping in different batteries: 9 V, 3 V coin cell, and 1.5 V AA battery. Use the picture below as a guide.
- Continue to the next step.
- Stuck?
**HINT:**Like the previous lesson, the voltage across the resistor might not EXACTLY match the battery voltage, but it will be pretty close. The battery acts like it has an internal resistor, which has its own voltage drop across it - leaving less for the circuit's resistor.

## Step 6: LED Circuit

Finally, we will show you why controlling current matters! Let's put an LED back in the circuit, and see what happens if too much current passes through.

- Start by making room in the circuit to place the LED. Delete the red wire between the multimeter and button and insert the LED. Complete the circuit with two shorter wires. You can use the picture above as a guide.
- If you haven't already, replace the battery with the 9V battery again.
- Finally, change the resistor value to 100 ohms using the dropdown menu.
- Simulate the circuit and press the button. A starburst icon appears on the LED indicating that too much current is passing through. The multimeter should read 65 mA, which is much higher than what the LED needs!
- A 100 ohm resistor is not strong enough to protect the LED. In the next step, we'll figure out how large this resistor should be to limit current appropriately.
- Continue to the next step.

## Step 7: Applying Ohm's Law

When you use LEDs in your circuits, you will always need a resistor to limit the current to a reasonable value. For most LEDs, you'll want to use the reported current rating. A typical value is 20 mA, and in the simulator this is the maximum value that the LED can handle!

Recall that the voltage across the LED varies with current running through it. This might sound really complicated, but the value of "forward bias" reported for your LED is the voltage drop associated with that ideal current. For us, that's 2.1 V.

In summary we have:

20 mA maximum current

2.1 V forward bias, or voltage drop

This is all the information you need to choose a good current limiting resistor using Ohm's Law!

- Remember that Ohm's law is applied to only one component: the resistor. Use the diagram above to confirm the voltage across the resistor. V = 9 - 2.1 = 6.9 V
- Recall that the current running through the resistor is the same as the current running through the LED. You'll need to convert units of milliamps (mA) to Amps (A). I = 20 mA = 0.02 A
- Resistance is unknown! Use Ohm's Law to calculate the resistance. R = V / I R = 6.9 / 0.02
- Click on the resistor and change its value to the number that you calculated! (see hint for answer.)
- Simulate the circuit. Does the LED light up without exploding? How much current is running through?
- Continue to the next step.
- Stuck?
**HINT:**The resistor should be 350 ohms A common mistake is to use the battery voltage as the value of V in Ohm's Law. Remember -- Ohm's Law applies to a single component in your circuit. You need to use the voltage across just the resistor. In this case it's ~6.9V.

## Step 8: Review

In this lesson, you learned how voltage, current, and resistance are mathematically related through Ohm's Law. This will be an extremely useful equation to keep in mind in future projects when you want to find out or control how much current is running through your components.

V = I x R

You also learned how to limit current through an LED using a 345 ohm resistor. Whenever you use an LED, you will want to use a resistor with at least this value with it! Keep this in mind, as it will be useful for the final project: Dimmer Switch.

- In your time remaining, you can replace the 9V battery with the 3V coin cell. Can you figure out what resistor is needed to protect the LED in this case? (see hint for solution.)
- Continue to the next lesson to do the project: Dimmer Switch!
- Stuck?
**HINT:**If the voltage drop across the LED is ~2.1, then the voltage drop across the resistor will be ~0.9. The maximum current through the LED is still 0.02 A. R = 0.9 / 0.02 = 45 ohms The results you see in the simulator might be a little different, but 45 ohms is a safe value to use with an LED and 3V battery to run the LED without burning it out.

**Next Lesson:**Dimmer Switch Project