The Math Behind Circuits

Materials

Background Information for Teachers

Vocabulary

• Circuit: A complete circular path that electricity flows through.
• Current: A flow of charged particles, such as electrons or ions, moving through an electrical conductor or space.
• Diagram: A graphical representation of an electrical circuit.
• Milliamp: A unit of measurement for an electric current flowing through an electrical conductor.
• Parallel circuit: A circuit where current is flowing in multiple branches at one time.
• Power: A source or means of supplying energy.
• Series circuit: A circuit where current is flowing in only one closed loop at a time.
• Schematic: A diagram using abstract, graphic symbols used by engineers to communicate information.
• Voltage: Electric potential or potential difference expressed in volts.

Prep Work

Lesson Preparation

1. Collect, organize, and set up materials.
2. Print the Circuit Scenarios Handout for Session 2 (one per team).
3. Build a couple of circuits yourself with other educators or kids you know. This will give you practice with the materials and tools to help anticipate student questions.

Lesson Instructions

Session 1

Introducing Circuitry Engineering (5 min)

1. Activate prior knowledge by exploring what learners already know about electrical power. Guiding Questions could include:
   • What are some items that you use that need electricity for power?
   • What are some things these items have in common (i.e., a switch or another way to activate the device)?
   • Can you think of any items that have multiple lights sharing a single power source (i.e., a string of holiday lights)?
2. Let learners know that today they are going to investigate the inner workings of electrical items by building circuits.

Circuit Exploration (20 min)

1. Divide learners into teams of two to four. Give each team one set of circuit materials.
2. Introduce the Circuit Exploration Challenges and give teams 10 minutes to explore the circuit materials and complete as many of the challenges as they can.

3. While teams are building circuits, walk around the room, troubleshoot, and support teams as needed. If teams are stuck on how to proceed, try asking open-ended questions, such as:
   • What have you tried?
   • What do you think your circuit needs?
   • What might be preventing the electricity from flowing through your circuit? Is everything connected?
4. Image Credit: Tech Museum After 10 minutes, bring the class back together to talk about what they discovered so far.
5. Take a quick poll to assess where teams are in the challenges. Let them know it is fine if they have not completed Challenges 3 and 4 as they will be exploring them more in the next section.
6. Ask teams to share their solutions for Challenge 2. Confirm that the way to light the bulb using the fewest components is with a power source, two wires, and a bulb.
   • Ask for a volunteer to draw their circuit on the board.
   • Trace the path the electricity is taking through the circuit components to show that everything is connected to something else (see Fig. 1 to the right).
7. Image Credit Let learners know that you will now show how an electrical engineer would draw the same circuit.
   • Draw the same circuit with schematics (See Fig. 2 to the right).
   • Ask students: Why might a schematic diagram be preferable to a drawing?
     • Discuss how diagrams are used to communicate information about the path of a circuit regardless of the language spoken by the engineer, allowing them to work with other engineers anywhere in the world.

Series and Parallel Circuits (15 min)

1. Pass out paper and pencils. Encourage students to troubleshoot their circuits by drawing a diagram or creating a schematic.
2. Give teams five more minutes to explore Challenge 3, light up 2 bulbs in two different ways. Bring the class back together when the time is up.
3. Ask for a volunteer to share one of their two-bulb circuits by drawing a diagram on the board. Then ask a volunteer from a different group to share a different example of a two-bulb circuit.
4. Label the appropriate diagrams as series circuit and parallel circuit. Confirm that all of the teams have built both kinds of circuits.
5. Ask students: What differences did you notice between the two types of circuits during your exploration? Responses may include:
   • The bulbs are brighter in the parallel circuit than in the series circuit.
     • This is because there is more voltage (and therefore more current) flowing to the bulbs in the parallel circuit.
   • The series circuit required three wires while the parallel circuit required four.
6. Explain the difference between series and parallel circuits.

Swipe left to see more

Series Circuit	Parallel Circuit
Image Credit: Tech Museum	Image Credit: Tech Museum
The electricity passes through each component in a single path before returning to the power source. The current through each of the components is the same. The voltage across the circuit is the sum of the voltages across each component.	There are different paths for the electricity to take, so the current splits depending on the resistance of each path. The total current is the sum of the currents through each component. The voltage across each of the paths is the same.

Diagramming and Building Circuits (15 min)

1. Draw a diagram of three bulbs in series circuits and three bulbs in parallel circuits on the board.
   Image Credit: Tech Museum
2. Teams will spend the next 15 minutes exploring Challenge 4, building and diagramming how to light up 3 bulbs in two different ways.
   • Ask teams to show you once they have completed each one.
   • Have teams draw a diagram of a three- (or more) bulb circuit they have built.
3. If teams finish building and diagramming their circuits early, have them trade diagrams with another team and try to build their circuit.
   • Supply teams with more wires and bulbs as needed.
   • Optional: Pass out switches, motors, fans or buzzers and challenge teams to add them into their circuits. If using fans teams will need to connect them to a motor first.

Debrief (5 min)

1. Lead a short debrief with some of these questions:
   • What did you find challenging about building circuits?
   • How did drawing the diagrams help your team understand how to build the circuits?
   • How do schematics help engineers communicate their ideas?

Key for Component Symbols

Image Credit: Tech Museum

Session 2

Introducing Circuit Calculations (5 min)

1. Ask for volunteers to briefly review what they learned about building circuits in the previous session.
2. Let students know that today they will be practicing some circuit calculations. Calculations will help them determine what is happening with their circuit, including the amount of current, voltage and energy.

Ohm's Law Image Credit: Tech Museum

If you are new to teaching circuit calculations, we recommend reviewing Ohm's Law prior to this lesson. Ohm's Law states that current through a conductor between two points is directly proportional to the voltage across the two points.

$$\frac{V}{R} = I$$

$$\frac{Voltage\: (volts)}{Resistance\: (ohms)} = Current\: (amps)$$

Practical Circuit Questions (35 min)

1. Use the tables below to help students work through a series of calculations needed to understand the circuits they explored in the last session.

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What is the total voltage of the batteries?
	Diagram	Question	Answer
Series Circuits Calculate the voltage in a series by adding the voltage in the batteries together.	Image Credit: Tech Museum	1.5V + 1.5V = X	Total voltage = 3V
Parallel Circuits Calculate the total voltage supplied in a parallel circuit by adding the voltage of the batteries in one branch together.	Image Credit: Tech Museum	1 branch = 1.5V	Total voltage = 1.5V
	Image Credit: Tech Museum	1 branch = 2 series batteries 1.5V + 1.5V = X	Total voltage = 3V

2. Once students understand the total voltage of the circuits they explored, have them consider:

   If you can use two 1.5V batteries in series to supply 3V, why would you use two pairs of two 1.5V batteries (four batteries total) to supply 3V to your circuit?

   • Remind them that, in addition to voltage, when looking at electrical components we also want to know how long they will last.
3. Use the table below to work through these calculations with students.

4. Ask students to determine how long two AAA batteries will last in series versus parallel.
   • In series, the battery voltage is constant across the entire circuit, so two batteries give the same mAh as one.
     • Ex: Two AAA batteries in a series = 750 mAh at 3V
   • In parallel, the battery voltage is constant across all the circuit branches, so they would need to add the mAh for each battery.
     • Ex: Two AAA batteries in parallel = 1,500 mAh at 1.5V
5. Revisit the question above: Based on our calculations, why would you use two pairs of two 1.5V batteries (four batteries total) to supply 3V to your circuit?
   • Two pairs of two 1.5V batteries in parallel will supply 3V to your circuit, but will last longer.

Practice Calculations (10 min)

1. Have students get back into their teams. Let them know that they are going to spend the next 10 minutes applying what they have learned about calculations to a few scenarios.
2. Pass out the Circuit Scenarios Handout and pencils.
3. Give teams 10 minutes to come up with solutions to the scenarios.
   • Encourage them to use diagrams and calculations to think through their ideas.
   • They should do this for both series and parallel battery connections.
   • Bring the whole group back together when the time is up.

Sharing Solutions (10 min)

1. Ask for teams to share their solutions for each of the scenarios.
2. Encourage them to share their thought process and calculations.
3. Sharing questions can include:
   • What process did you use to make that decision?
   • How did you use the calculations and math to determine your answer?
   • Where do you think these types of calculations get used in the real world?