# Constructing an Understanding of Electric Circuits

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## Introduction: Constructing an Understanding of Electric Circuits

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This instructable is of a unit I do with my honors physics students to help them construct for themselves an understanding of how every part of an electric circuit works, and why it does what it does. I have broken down the unit into a series of objectives with an explanation of what students do to achieve that objective. The inspiration for this series of investigation is the CASTLE curriculum which was written by a committee of physics teachers in the 1980's.

An inexpensive source of mini incandescent bulbs is older strings of holiday lights. As people replace their holiday lights with lower energy LED lights, ask for their old light strings. All you have to do is cut apart the lights and strip the ends of the wires. These holiday bulbs are very sturdy and difficult to blow out even if students connect them to more batteries then they should during their investigations.

The unit is broken into a series of research questions:

What is the minimum needed to light an incandescent bulb?
Is there anything happening in the wires of a circuit when a light bulb is lit?
Which materials are insulators and which are conductors?
How does an incandescent bulb work?
How do resistors effect the charge flow through a circuit?
How do the resistance of your two different types of bulb and connecting wire compare?
How is the total resistance of your circuit effected by adding a bulb in parallel?
What does a capacitor do in a circuit?
What does a generator do in a circuit?
Does a battery have internal resistance?
What causes electric potential difference changes in the wires?
How does electric potential difference (volts) divide among components in a series circuit?
How does electric potential difference (volts) divide among components in a parallel circuit?
How does current vary around a series circuit?
How does current vary among the branches of a parallel circuit?
Do flow paths influence the electric potential difference between battery terminals?
How does voltage vary as a capacitor charges?
How do you use a voltmeter and an ammeter to make measurements in a circuit?

At the beginning the investigation questions are followed by more detailed instructions as to how to answer that question, but as the investigations continue less and less guidance is given for the students as they build their mental model of how electric circuits operate. I give quizzes after each five questions to make sure that students are building appropriate knowledge and gathering sufficient evidence for their model to correctly interpret what is happening in the circuits.

## Step 1: What Is the Minimum Needed to Light an Incandescent Bulb?

Learning Objective:
• Determine what the minimum requirements are to light an incandescent bulb.

Materials: mini incandescent bulb, bulb socket, battery case, D cell batteries, connecting wires

Design a circuit that contains the minimum materials needed to light an incandescent bulb. (You do not need to use all of the investigation 1 materials for this circuit.)

Lab questions
1.  Build a circuit with three D-cell batteries and two mini incandescent bulbs in a closed loop. Break the loop by disconnecting a wire from one end of the battery holder and then reconnect it.  Do both bulbs appear to light at exactly the same time?  Do you believe that both bulbs actually light at the same time?
2.  Reconnect the wire to the battery, and then disconnect a different wire somewhere else in the loop.  Try this in several places.  Is there any place where you can break the loop and one or both of the bulbs will still stay lit?
3.  Unhook one of the wires and bring it as close as you can to where it was connected  without actually making contact.  Do this slowly and carefully, watching the space between the wire and the contact point. Do the bulbs light? Do you think actual contact is needed for the bulbs to light continuously?

## Step 2: Is There Anything Happening in the Wires of a Circuit When a Light Bulb Is Lit?

Learning Objective:
• Students will look for experimental evidence to support or refute that something is happening in the wires when a light bulb is lit.
Materials: mini incandescent bulbs, bulb sockets, battery cases, D cell batteries, connecting wires, compass

A compass is a small magnet suspended so that it can rotate freely if placed in an electric or magnetic field. This means that a compass can be used to detect electrical activity in wires. To use the compass in this manner follow these instructions:

1.  Place the compass on your table, away from any metal parts of the table such as table legs or bolts.  Tape the compass to the table so its orientation does not change during use. The compass is not connected to any wire, it is just acting as a detector to visualize what if anything is happening in the wires.
2.  Connect two bulbs and and three batteries into a closed loop circuit. Stretch the loop out as far as possible; keep the battery as far from the compass as you can.  (The steel case of the D-cells becomes magnetized with use and will interfere with the compass reading.)
3.  Disconnect one wire in the loop.  Lay a wire from the circuit on top of the compass and align this wire parallel to the needle of the compass and directly over the needle.   Connect and disconnect the circuit several times while watching the compass needle.

Lab Questions
1.  Does the compass needle deflect clockwise or counter-clockwise when you connect the wire to close the loop?  What happens to the compass needle when the battery is disconnected?
2.  Is there any evidence that something is happening in the wire over the compass during the time the loop is broken?  What is the evidence, for or against this?

Do not move the compass.  Break the loop and rotate the entire loop – the  battery, sockets and wires together – so that the next wire in the circuit is now over the compass and parallel to the needle.  Be certain the loop is stretched out so the battery is as far as possible from the compass. Before you connect the wire, predict what compass deflection you will observe when you close the loop. Connect and disconnect the loop, and observe the compass needle.

3.  Does the compass deflect in the same direction as it did under the first wire?  Does it deflect by the same amount?
4.  Rotate the entire loop again, so that the next wire is over the compass.  Predict what you will observe when you connect and disconnect the loop again, and observe the compass.  Then try it. What happened to the compass needle?  How does this compare to its behavior under the other two wires? Do you think the same thing is happening in the wires all the way around the loop?  Why?
5. Reverse the orientation of the battery by disconnecting the wires from the battery and then reconnecting them at opposite ends of the battery.  Before doing so, predict what you will observe. What needle deflection do you observe when you close the loop after you reverse the battery orientation?  What do you observe when you break the loop? How does this compare with your previous results?

Reflection Questions
Discuss the answers to each of these questions with your lab group. The evidence for these answers is to be based upon the observations you made during your investigations.

1.  What do you think might be happening in the wires to make the compass deflection change direction when the battery orientation is reversed?
2.  Some people suggest that there is something moving in the wires.  Is there any direct evidence of this?
3.   If something is moving in the wires, does the direction of movement and the amount of movement appear to be the same in every wire of the circuit at one time?  What is the evidence?
4.  What do you think the battery does in this circuit?  What is the evidence? Can a compass be used to identify the direction of movement within a wire?

## Step 3: Which Materials Are Insulators and Which Are Conductors?

Learning Objective:
• Identify specific materials as insulators or conductors of electric current.
Materials: mini incandescent bulbs, bulb sockets, batteries, battery cases, connecting wires, miscellaneous objects to test for their ability to conduct electric current

Design a testing circuit to determine whether common household objects are insulators or conductors. Use your circuit to test several objects you have on hand, one of the objects you test must be graphite.

Lab Questions
Discuss the answers to each of these questions with your lab group.

1.  Do most or all of the conductors have something in common?  If so, what?
2.  Do most or all of the insulators have something in common?  If so, what?

## Step 4: How Does an Incandescent Bulb Work?

Learning Objective:
• Determine how an incandescent bulb works.

Materials: mini incandescent bulb, bulb socket, batteries, battery cases, connecting wires, compass, dissected household incandescent bulb

Analyze the parts of an incandescent bulb to determine how it works. As part of your investigation determine whether each part of the bulb is an insulator or conductor and explain why the bulb socket is constructed the way it is. Be careful when you test the filament, the filament is very delicate and may produce smoke or flames when you put it into the circuit.

Reflection Questions
1.  What evidence suggests that something happens in the wires when the bulbs are lit?
2.  What happens in the wires when the battery connections are reversed?  What is your evidence?
3.  What is the battery doing when the bulbs are lit?
4.  Based on the assumption that something flows through wires when bulbs are lit in a circuit, is the direction of the flow the same in all the wires, or does it vary in different parts of the circuit?  What is the evidence for your answer?
5.  What materials and conditions must be present for a bulb to light?
6.   On a cross-section diagram of a bulb in its socket, draw a line to show a continuous conducting path that starts at a wire attached to one clip, goes through the bulb and exits through a wire at the other clip.

Instructions for Dissecting a Household Incandescent Bulb
I don't allow the students to do this for themselves, I prepare the dissected bulbs for them. Here are the preparation steps:

1. Find some old incandescent bulbs. Many people have bags of them in their garage or attic from when they switched out their bulbs to fluorescent and didn't know what to do with them.
2. Put on your safety goggles just in case the bag breaks when the bulb breaks. Hold the bulb by the metal end and put the glass end into a brown paper lunch bag.
3. Gather the brown bag carefully around the metal end so the bag is completely closed.
4. Rest the bulb (inside the bag still) on a table and gently tap it with a hammer until it shatters.
5. Carefully open the bag and shake any broken glass pieces down into the bag. Don't let go of the metal end.
6. If the break went well, you should have a significant portion of the filament left intact. Handle the bulb carefully as just moving it too fast will shake the filament to pieces.
7. Be sure to discard the broken glass pieces properly. I do this at school where we have a sharps container.
8. If there are large shards of glass sticking on the metal end of the bulb, you can use a needle nose pliers and carefully break them away from you into the bag.

## Step 5: How Do Resistors Affect the Charge Flow Through a Circuit?

Lesson Objectives:
• Compare the charge flow through circuits with different amount of resistance.
Materials: resistors, mini incandescent bulbs, bulb sockets, batteries, battery cases, connecting wires, compass

The amount and direction of compass deflection can be used to measure the current (charge flow rate) through the circuit. Complete an investigation to determine how resistors connected in a series circuit (a loop) affect the charge flow through a circuit.

## Step 6: How Do the Resistance of Your Two Different Types of Bulb and Connecting Wire Compare?

Lesson Objective:
• Compare the resistance of different bulbs and connecting wires.
Materials: two different mini incandescent bulbs, bulb sockets, batteries, battery cases, connecting wires, compass, dissecting microscope or magnifying lens

As part of your investigation, construct a circuit that has one each of two different mini incandescent bulbs, and three batteries in a simple loop circuit. Explain why you observe what you observe when you connect this circuit. Construct any additional circuits you need to answer the question posed in this investigation.

Visualize Resistance: Resistance of straws and coffee stirrers
Cut a drinking straw to the same length as a coffee stirrer. Take a breath, and note the time it takes you to completely exhale through the drinking straw. Then repeat with the coffee stirrer. How do the exhalation times compare between the two straws? Why do you see this?

Tape two and then four coffee stirrers together end to end (like a series circuit) and record the time required to exhale one full breath through each of these lengths.

Hold four coffee stirrers parallel to each other and exhale through all four coffee stirrers (like a parallel circuit). How does the time it takes to exhale through the coffee stirrers in parallel compare to the time it takes to exhale through one coffee stirrer?

Look at the filaments of each of the types of bulbs under a dissecting microscope or hand lens. Compare the thickness and length of the filaments and relate that to the observations you made when you connected a circuit with one of each of these types of bulbs.

Lab Questions
1.  How do the effect of tube diameter on air flow compare to the effect of bulb filament diameter on the rate of charge flow?
2.  How does the length of a conducting tube influence the rate of flow through that tube when the coffee stirrers are connected in series?

## Step 7: How Is the Total Resistance of Your Circuit Affected by Adding a Bulb in Parallel?

Lesson Objective:
• Determine how the total resistance of a circuit is affected by adding a bulb in parallel.
Materials: mini incandescent bulbs, bulb sockets, batteries, battery cases, connecting wires, compass

Begin your investigation with this pair of circuits. Connect a circuit with 2 D-cells and two identical mini incandescent bulbs. Add a third mini bulb by connecting it in parallel to one of the first two bulbs and observe.  Use a compass to detect the change in charge flow when the third bulb is added.

## Step 8: What Does a Capacitor Do in a Circuit?

Lesson Objectives:
• Investigate what a capacitor does in a circuit.
• Investigate how a capacitor is constructed.
Materials: mini incandescent bulbs, bulb sockets, batteries, battery cases, connecting wires, compass, 0.025 F capacitor, 0.1 F capacitor, stopwatch, dissected capacitor

Capacitors have positive and negative ends and must be connected to the battery in the correct orientation to operate properly. Each capacitor specifies the maximum electric potential difference (voltage) that can be safely connected to the capacitor, please do not exceed this limit. The negative lead of the capacitor is labeled, this end is connected to the positive end of the battery.

Design and complete an investigation to determine what a capacitor does in a circuit. An important piece of evidence for these investigations is the time it takes to charge and discharge the capacitor. Begin your investigation by connecting these two circuits:
• Connect three D cell batteries, two mini incandescent bulbs, and the capacitor all in series and use the compass to observe what is happening with charge flow once the batteries are connected.
• Once the charge flow has stopped, disconnect the batteries but leave the rest of the circuit intact. Connect the two wires that were connected to the battery to each other and use the compass to observe what is happening with charge flow.

As you continue your investigation, explore circuits with different numbers of batteries in the charging circuit, bulbs of different resistances, bulbs in parallel with the capacitor, and borrow a capacitor from another lab group to explore capacitors in series and in parallel with another when the capacitors are identical and when they are different.

Lab Questions
1.  Are the bulbs lit longer when charging the 0.025 F capacitor or the 0.1 F capacitor through the same circuit? Why do you think this happens?
2.  Does the charge that flows into the capacitor during charging get used up in the capacitor? Or does it get stored somewhere in the capacitor?  How do you know?
3.  Is the same thing happening in every wire during charging?  Is the same thing happening in every wire during discharging?  What is the evidence?
4.  Where do you think the charge comes from that lights each of the bulbs during capacitor charging?
5.  Where do you think the charge comes from that lights each of the bulbs during discharging?
6. When two identical capacitors are connected in series to each other, do they store more or less charge than they do individually? What about in parallel? What is your evidence?
7. When two different capacitors are connected in series to each other, do they store more or less charge than they do individually? What about in parallel? What is your evidence?

## Step 9: Does a Battery Have Internal Resistance?

Lesson Objective:
• Determine whether or not a battery has internal resistance.
Materials: mini incandescent bulbs, bulb sockets, connecting wires, compass, stopwatch, D cell batteries, battery cases, run down D cell batteries

Design and complete an investigation to answer the question posed by this investigation.

## Step 10: What Causes Electric Potential Difference Changes in the Wires?

Lesson Objective:
• Determine what causes electric potential difference changes in a wire in a circuit.
Materials: mini incandescent bulbs, bulb sockets, connecting wires, compass, stopwatch, 0.22 F capacitor, 0.1 F capacitor, D cell batteries, battery cases

Use the circuit in the diagram for your investigation.

The capacitor will slow down the rate of charge flow so you can see what happens when you connect the battery to the circuit. Compare this circuit to the same circuit without the capacitor and explain which bulbs light first when the batteries are connected to the circuit without the capacitor and why these light first.

Lab Questions
1.  At the instant of connection:
a)  Is there any movement through the wire between the two bulbs in parallel with the capacitor?
b)  Where does the charge come from that passes through the bulb in the top of the diagram?
2.  As the charge moves through the glowing bulbs, what electric potential differences changes occur in the circuit?
3.  Did you observe a change of bulb brightness when you removed the capacitor from the circuit?  Why or why not?
4.  How do you think a circuit with four bulbs in series gets to its final steady state condition without a capacitor?

## Step 11: How Does Electric Potential Difference (volts) Divide Among Components in a Series Circuit?

Learning Objective:
• Investigate how electric potential difference divides among the components in a series circuit.

Materials: mini incandescent bulbs of two different resistances, bulb sockets, connecting wires, compass, D cell batteries, battery cases, voltmeter

Design and complete an investigation to determine mathematically how the electric potential difference supplied by the battery is divided among the components in a series circuit. Voltmeters are always connected in parallel to the portion of the circuit for which you wish to measure the electric potential difference.

Why do they have to be connected this way to make an accurate measurement?

## Step 12: How Does Electric Potential Difference (volts) Divide Among Components in a Parallel Circuit?

Learning Objective:
• How does electric potential difference divide among components in a parallel circuit?
Materials: mini incandescent bulbs of two different resistances, bulb sockets, connecting wires, compass, D cell batteries, battery cases, voltmeter

Design and complete an investigation to determine mathematically how the electric potential difference supplied by the battery is divided among the components in a parallel circuit.

## Step 13: How Does Current Vary Around a Series Circuit?

Learning Objective:
• How does current vary around a series circuit?
Materials: mini incandescent bulbs with two different resistances, bulb sockets, connecting wires, compass, D cell batteries, battery cases, ammeter

Design and complete an investigation to determine mathematically how the current supplied by the battery flows through the components in a series circuit.

To measure current with an ammeter you have to break the circuit and connect the ammeter in series where you want to measure the current. An ammeter will be damaged and possibly destroyed if connected improperly, if you are not sure of how to connect it ask your teacher before connecting your batteries.

Why do they have to be connected this way to make accurate measurements? Why will connecting an ammeter improperly damage or destroy an ammeter?

## Step 14: How Does Current Vary Among the Branches of a Parallel Circuit?

Learning Objectives:
• Determine how the current varies among the branches of a parallel circuit.

Materials: mini incandescent bulbs of two different resistances, bulb sockets, connecting wires, compass, batteries, battery cases, ammeter

Students are to design and complete an investigation to determine mathematically how the current supplied by the battery flows through the components in a parallel circuit. It is important for students to record what circuits they used and what current measurements they made on those circuits.

Discussion Questions
Discuss these questions with your lab group.

1. Do multiple mini bulbs of the same resistance connected in parallel to each other present an easier or more difficult flow path than a single bulb? Justify your response with evidence from your investigation.
2. Which has a greater electric potential difference across it, two identical bulbs in parallel or a single one of those bulbs connected to the battery? Justify your response with evidence from your investigation.
3. How does the current divide between multiple branches of a parallel circuit if the bulbs are not identical? Justify your response with evidence from your investigation.

## Step 15: Do Flow Paths Influence the Electric Potential Difference Between Battery Terminals?

Learning Objectives:
• Determine if the total resistance connected to a battery effects the electric potential difference between the battery terminals.

Materials: mini incandescent bulbs, bulb sockets, connecting wires, compass, D cell batteries, battery cases, voltmeter

Design and complete an investigation to answer the question posed by the investigation. Be sure to record a schematic diagram documenting the circuits you constructed and the measurements you took of those circuits.

Research how disposable batteries produce an electric potential difference between their terminals and reconcile this explanation with what you found in your investigation. Be sure to document your sources.

## Step 16: How Does Voltage Vary As a Capacitor Charges?

Learning Objectives:
• determine how mathematical relationship between voltage and time as a capacitor charges and as it discharges.
• determine how the total resistance of the circuit affects the charging rate of a capacitor.
• determine how the capacitance of a capacitor affects the charging rate of a capacitor.

Materials: two different resistance mini bulbs, bulb sockets, D cell batteries, battery cases, connecting wires, 0.025 F capacitor, 0.1 F capacitor, labpro, voltage probe, computer with Logger Pro software

Predict the shape of the curve for the voltage vs. time for a capacitor charging and one for a capacitor discharging.

Connect a simple series circuit with one capacitor and record the voltage vs. time while the capacitor is charging and then discharging. Use a computer interface and voltage probe to record the electric potential difference over the capacitor as it charges and discharges. Compare your results to our predictions and explain why they are shaped the way they are.

Design and complete an investigation to determine how the total resistance of a circuit affects the shape of this curve and the charging rate of a capacitor.

Design and complete a second investigation to determine how the total capacitance of a circuit affects the shape of this curve and the charging rate of a capacitor. Use the curve fitting function of the software to find the equation for the curve and relate that to the variables you are changing.

## Step 17: How Do You Use a Voltmeter and an Ammeter to Make Measurements in a Circuit?

Learning Objectives:
• determine how electric potential difference is measured in a circuit.
• explain why electric potential difference must be measured in this manner.
• determine how current is measured in a circuit.
• explain why current must be measured in this manner.
• using electric potential difference and current calculate the resistance of each of the types of bulbs you have been using in these investigations.
• practice using Kichoff's Rules to analyze the current and electric potential difference throughout a circuit.
Materials: digital multi-meter, connecting wires, mini incandescent bulbs, bulb sockets

Set up a sequence of series circuits to analyze the trend in current and electric potential throughout a series circuit using the meter to measure current in several locations throughout the circuit and electric potential over several components throughout the circuit.

Set up a sequence of parallel circuits and then combination circuits (circuits that have components that in series and components that are in parallel) to do the same. Compare your results to Kirchoff’s Rules to see if they agree with the rules. During your investigation determine the resistance of each of the types of bulbs we were using in our investigation.

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