South Pasadena • Physics
Name
10 · Circuits
Period
TUTORIAL: A MODEL
Date
FOR CIRCUITS
Tutorial Instructions
This Tutorial contains “Activities” and “Exercises.”

Activities: These are intended to be completed in groups with the appropriate laboratory equipment in the
classroom, and the results are reviewed by the teacher.

Exercises: These are intended to be completed individually at home using the conclusions drawn from the
Activities.
As you complete these pages,


The elements in a circuit are drawn:
o
A battery looks like this:
The longer line indicates the positive (+) terminal; the shorter line indicates the negative (–) terminal.
o
A light bulb looks like this:
When the instructions ask to rank, use order symbols such as <, ≤, =, ≥, and >. Be precise (for example, <
and ≤ are different and are not interchangeable).
o

Bulb A = Bulb B < Bulb C = Bulb D
When the instructions ask to describe or explain (i.e. whenever the response space uses a dotted line
), write your response in a complete sentence, using prepositional phrases to precisely describe the
subject. Avoid using pronouns (i.e. it, they). Here are poor responses:
o
Nothing.
o
It was bright.
o
The current is bigger.
Here are some better responses:

o
The bulbs did not light up.
o
Bulb A lit up brightly.
o
The current through bulb A is greater than that through bulb B.
A note about prepositions:
o
Resistance:
The resistance of bulb X …
o
Potential difference:
The potential difference across bulb X …
o
Current:
The current through bulb X …
These activities and exercises are challenging. Do not merely go through the motions to simply complete them.
Take the time to develop a mental model of what is going on.
1
Class Summaries
Current
Resistance
Potential Difference
Single Bulb
In Series
In Parallel
This tutorial and exercises are adapted from:
McDermott, Lillian, Peter S. Shaffer, and the Physics Education Group. Tutorials in Introductory Physics. 1st Ed.
Upper Saddle River, New Jersey: Prentice-Hall, Inc., 2002. Print.
McDermott, Lillian, Peter S. Shaffer, and the Physics Education Group. Tutorials in Introductory Physics:
Homework. 1st Ed. Upper Saddle River, New Jersey: Prentice-Hall, Inc., 2002. Print.
2
Activity 1: Complete Circuits (in class)
1. With just one wire, one light bulb, and one battery, make the light bulb light. Connect these in a variety of
ways.
a. Sketch at least four arrangements that light the bulb, and at least four arrangements that do not light the
bulb.
A battery looks like:
A bulb looks like:
Wire looks like:
Arrangements that do light the bulb
Arrangements that do not light the bulb
b. What two parts of the bulb need to be touched by the wire in order for the bulb to light?
(1)
(2)
c. What two parts of the battery need to be touched by the wire in order for the bulb to light?
(1)
(2)
d. State the requirements that must be met in order for the bulb to light.
e. When the bulb is lit, you created a circuit. Why is circuit a particularly good name for this?
3
2. A student has briefly connected a wire across the terminals of a battery until the wire
feels warm. The student finds that the wire seems to be equally warm at points 1, 2,
and 3.
3
Based on this observation, what might you conclude about the current through the
wire at one place compared to another?
1
2
3. Light a bulb using a battery and a single wire.
a. Observe and record the brightness of the bulb (i.e. dark, dim, bright) when objects made out of various
materials (e.g. paper, coins, pencil, lead, eraser, your finger) are inserted into the circuit.
Material
Brightness
b. What is similar about most of the objects that let the bulb light?
4. Carefully examine a bulb. Two wires extend from the filament of the bulb into the base.
You probably cannot see into the base, however, you should be able to make a good
guess as to where the wires are attached.
a. Draw how the wires are attached in the bulb to the right.
b. Describe where the wires are attached. Explain based on your observations in parts 1-3.
On the basis of the observations that we have made, we will make the following assumptions:

A flow exists in a complete circuit from one terminal of the battery, through the rest of the circuit, back to the
other terminal of the battery, through the battery, and back around the circuit. We will call this flow electric
current.

For identical bulbs, bulb brightness can be used as an indicator of the amount of current through the bulb: the
brighter the bulb, the greater the current. More flow, more glow!
Starting with these assumptions, we will develop a model that we can use to account for the behavior of simple
circuits. The construction of a scientific model is a step-by-step process in which we specify only the minimum
number of attributes that are needed to account for the phenomena under consideration.
4
Activity 2: Current and Resistance of Bulbs in Series (in class)
1. Set up a two-bulb circuit with identical bulbs connected one after the other as shown. Bulbs
connected in this way are said to be connected in series.
A
a. Describe the brightness of the two bulbs (i.e. dark, dim, or bright).
Bulb A is
. Bulb B is
B
.
The brightness of Bulb A is roughly [ less than | the same as | greater than ] that of Bulb B.
b. Is the current “used up” in one bulb, or is the current the same through both bulbs? Explain.
c. Do you think that switching the order of the bulb might make a difference?
Check your answer. Did it make a difference?
[ Yes | No ]
[ Yes | No ]
d. On the basis of your observations alone, can you tell the direction of the flow through the circuit?
[ Yes | No ]
2. Set up a single-bulb circuit, as shown on the right.
a. Rank Bulbs A, B, and C in order of increasing brightness.
C
b. How does the current through a bulb in a single-bulb circuit compare with the current through the same
bulb when it is connected in series with a second circuit? Explain your reasoning based on part a.
c. How does the current through the battery in a single-bulb circuit compare to the current through the
battery in a two-bulb series circuit? Explain your reasoning based on part b.
d. We may think of a bulb as presenting an obstacle, or resistance, to the current in the circuit. Would
adding more bulbs cause the total resistance to increase, decrease, or stay the same as before?
e. Formulate a rule for predicting how the current through the battery would change (i.e. whether it would
increase, decrease, or remain the same) if the number of bulbs connected in series were increased or
decreased.
5
Activity 3: Current and Resistance of Bulbs in Parallel (in class)
1. Set up a two-bulb circuit with identical bulbs so that their terminals are connected
together as shown. Bulbs connected together in this way are said to be connected in
parallel.
D
E
a. Describe the brightness of the two bulbs (i.e. dark, dim, or bright).
Bulb D is
. Bulb E is
.
The brightness of Bulb D is roughly [ less than | the same as | greater than ] that of Bulb E.
b. Describe the current through the entire circuit based on your observations. Specifically, describe the
current through the battery, through bulb D, and through bulb E. How does the current through the
battery seem to divide and recombine at the junctions of the two parallel branches?
2. Compare the bulbs in the single-bulb circuit (Bulb C) and the bulbs in the two-bulb parallel circuit (Bulbs D
and E).
a. Rank Bulbs C, D, and E in order of increasing brightness.
b. How does the current through the battery in a single-bulb circuit compare to the current through the
battery in a two-bulb parallel circuit? Explain your reasoning based on your observations.
c. Formulate a rule for predicting how the current through the battery would change (i.e. whether it would
increase, decrease, or remain the same) if the number of bulbs connected in parallel were increased or
decreased based on your observation of the behavior of the two-bulb parallel circuit and the model for
current.
d. How does the total resistance of a circuit change as the number of parallel branches is increased or
decreased?
6
Activity 4: Formulating our Model (in class)
1. How does the amount of current through a battery depend on the number of bulbs in the circuit and how they
are connected?
2. Unscrew one of the bulbs in the two-bulb parallel circuit. How does this change affect the current through the
branch that contains the other bulb?
A characteristic of an ideal battery is that the branches connected directly across it are independent of one
another.
3. The circuit on the right contains three identical bulbs and an ideal battery.
Assume that the resistance of the switch, when closed, is negligible.
a. Without setting up the circuit, make a prediction and rank the brightness of
the bulbs in the circuit with the switch closed.
b. Explain your ranking above.
c. Predict how the brightness of bulb F changes when the switch is opened. Explain.
d. Predict how the brightness of bulb G changes when the switch is opened. Explain.
7
F
G
H
Exercises A: Current and Resistance (at home)
1. In the diagrams, boxes have been drawn around the networks of bulbs in each circuit.
On the basis of your observations and the rule you developed relating current through the battery to total
resistance, rank the networks (boxes) A–C according to their equivalent resistance.
Explain your reasoning based on the model. (Do not use math.)
2. Use the model for electric current, rank the
networks shown below in order of increasing
resistance.
Explain your reasoning.
3. The circuit shown has four identical light bulbs and an ideal battery.
Rank the brightness of the bulbs.
Explain your reasoning.
8
4. A wire is now added to the circuit from part 3 above as shown to the right.
a. The brightness of Bulb C [ increases | remains the same | decreases ].
Explain your reasoning.
b. The brightness of Bulb A [ increases | remains the same | decreases ].
Explain your reasoning.
c. The current through the battery [ increases | remains the same | decreases ].
Explain your reasoning.
5. Consider the five networks shown to the right.
a. Rank the networks according to their equivalent resistance. (Hint:
Imagine placing each network in series with an indicator bulb and a
battery.)
b. How does adding a single bulb to the circuit in series with another
bulb or network affect the resistance of the circuit?
c. How does adding a single bulb to a circuit in parallel with another bulb or network affect the resistance of
the circuit?
9
6. The networks A-E in part 5 (above) are connected, in turn, to identical
batteries as shown. Use the model we have developed to:
a. Rank the circuits according to equivalent resistance.
Explain your reasoning.
b. Rank the circuits according to the current through the battery.
Explain your reasoning.
7. The circuit to the right shows four identical bulbs connected to an ideal battery.
a. Rank the bulbs in order from brightest to dimmest.
Explain how you determined the ranking.
b. Suppose that a switch has been added to the circuit as shown.
When the switch is opened, the current through bulb A will [ increase | remain
the same | decrease ].
Explain your reasoning.
10
Activity 5: Current and Resistance (in class)
Do not set up any circuits for this Activity.
1. The circuits at the right contain identical batteries, bulbs and unknown
identical elements labeled X.
a. How do the bulbs compare in brightness? Explain.
b. In each circuit, how does the current through the bulb compare to the current through element X?
Explain.
2. The circuits at the right contain identical batteries and bulbs. The boxes
labeled X and Y represent different unknown elements. (Assume there
are no batteries in either box.) It is observed that the bulb on the left is
brighter than the bulb on the right.
a. Based on this observation, how does the resistance of element X compare to that of element Y? Explain.
b. In each circuit, how does the current through the bulb compare to the current through the unknown
element?
c. In each circuit, how does the current through the bulb compare to the current through the battery?
3. A dashed box has been drawn around the network of
circuit elements that is in series with each of these
bulbs, B1, B2, and B3.
a. Predict the relative brightness of bulbs B1, B2, and
B3 in the circuits shown.
b. How do the currents through the batteries compare? Explain.
11
Activity 6: Potential Difference (in class)
Use two batteries in the circuits for this Activity.
A
1. Set up the circuit with a single bulb and the battery combination as shown.
a. Connect each probe of the voltmeter to a different terminal of
the battery to measure the potential difference across the battery. Then
make a similar potential difference measurement across the bulb.
Vbattery
VBulb A
b. How does the potential difference across Bulb A compare to the
potential difference across the battery?
2.
Set up the circuit containing two bulbs in series as shown.
B
a. Rank from largest to smallest the currents through bulbs A, B, and C.
C
Explain your reasoning.
b. Measure the potential difference across each element
in the circuit.
Vbattery
VBulb B
VBulb C
c. How does the potential difference across the battery
in this circuit compare to the potential difference across the battery in the single-bulb circuit (part 1a)?
d. Rank the potential differences across bulbs A, B, and C.
e. What is the relationship between the brightness of the bulb and the potential difference?
3. Suppose you measured the potential difference across both bulbs B and C, at the points
indicated.
B
a. Predict what the voltmeter would read. Explain.
C
b. How does the potential difference across the network of bulbs compare to the potential
difference across the battery?
12
4. Set up the circuit with two bulbs in parallel as shown.
D
E
a. Rank the current through bulbs A, D, and E.
Explain your reasoning.
b. Measure the potential difference across each circuit
element.
Vbattery
VBulb D
VBulb E
c. How does the potential difference across the battery in this circuit compare to the potential difference
across the battery in the single-bulb circuit?
d. Rank the potential difference across bulbs A, D, and E.
e. What is the relationship between the brightness of the bulb and the potential difference?
5. Answer the following questions based on the measurements you have made so far.
a. Does the current through the battery depend on the circuit to which it is connected?
[ Yes | No ]
Explain.
b. Does the potential difference across the battery depend on the circuit to which it is connected?
[ Yes | No ]
Explain.
13
Activity 7: Extending the Model (in class)
Our model for electric circuits includes the idea that, for identical bulbs, the brightness of a bulb is an indicator of
the current through the bulb. Based on our observations, we can extend the model to include the idea that, for
circuits containing identical bulbs, the brightness of a bulb is also an indicator of the potential difference across
the bulb.
F
1. Set up the circuit with three bulbs as shown and observe their brightness.
a. Without making voltage measurements, predict the ranking of the potential
difference across the battery and each bulb for the circuit on the right.
G
H
VBulb G
VBulb H
Explain your reasoning.
b. Measure the potential difference across each element in
the circuit. Make sure your measurements are
consistent with your predictions.
Vbattery
VBulb F
2. Consider the circuit to the right.
K
a. Without setting up the circuit, predict the ranking of the currents
through the battery and each bulb (Ibattery, IBulb J, IBulb K, IBulb L).
J
L
Explain your reasoning.
b. Predict the voltmeter measurements across each of the
elements in the circuit shown.
Vbattery
VBulb J
VBulb K
VBulb L
Vbattery
VBulb J
VBulb K
VBulb L
Explain your reasoning.
c. Set up the circuit and check your predictions. Make
sure your measurements are consistent with your
predictions.
14
3. Both circuits have more than one path for the current.
a. Sketch the possible current loops on the diagrams. (A “current loop” is a single path of conductors that
connect one side of the battery to the other.) Then for each loop, calculate the sum of the potential
differences across the bulbs in that loop using the measurements you made.
Current
Loop
Sum
of V
b. How do the sums of the potential differences across the bulbs in each loop compare to the potential
difference across the battery?
15
Exercises B: Potential Difference (at home)
1. The circuit to the right consists of a bulb in series with an electrical “black box.”
The following are possible contents for the “black box.” All the bulbs are
identical. Box C consists of a single piece of wire.
Suppose that each of the five boxes is placed, in turn, into the circuit. (Only one box is in the circuit at a
time.)
a. Draw the five circuit diagrams below. Show the contents of the boxes in place of the box itself.
b. Rank the five circuits according to the brightness of the indicator bulb in those circuits.
Explain your reasoning.
c. Rank the boxes according to their equivalent resistance.
Explain your reasoning.
16
Parts 2-4: Box A and box B contain unknown combinations of light bulbs. Bulb 1 is identical to bulb 2. The
batteries are ideal.
2. In the circuit to the right, the voltage across bulb 1 and the voltage across box A
are equal.
a. What, if anything, can you say about the resistance of box A compared to
the resistance of bulb 1? Explain.
b. Write an expression for the voltage across the battery (Vbatt) in terms of the voltage readings across box A
and across the bulb (VBox A,VBulb 1).
3. In the circuit to the right, the voltage across bulb 2 and the voltage across box B are
equal.
a. What, if anything, can you say about the resistance of box B compared to the
resistance of bulb 2? Explain.
b. Write an expression for the voltage across the battery (Vbatt) in terms of the voltage readings across box B
and across the bulb (VBox B, VBulb 2).
4. Box A and box B are now interchanged. It is observed that bulb 2 is now brighter than it was when box B
was in that circuit.
a. The resistance of box A is [ greater than, equal to, less than ] the resistance of box B.
Explain.
b. The current through battery 1 has [ increased | remained the same | decreased ].
c. The current through battery 2 has [ increased | remained the same | decreased ].
17
5. The bulbs in the circuit to the right are identical and the battery is ideal.
a. Rank bulbs A, B, and C in increasing brightness.
Explain.
b. Rank the voltages across the bulbs.
Explain.
c. Write an equation that relates the voltage across bulbs A and B to the battery voltage.
d. The voltage across bulb A is [ greater than, equal to, less than ] one-half the battery voltage.
Explain.
6. Suppose a student cuts the wire in the circuit from part 5 as shown to the right.
a. Rank the bulbs A, B, and C in increasing brightness.
Explain.
b. Rank the voltages across the bulbs.
Explain.
c. Write an equation that relates the voltage across bulbs A and B to the battery voltage.
d. The voltage across bulb A is [ greater than, equal to, less than ] one-half the battery voltage.
Explain.
18
7. Consider the following discussion between two students regarding the change in the circuit when the wire in
the circuit is cut, from part 6.
Student 1: “I think that bulb B will get brighter. Bulb B used to share the current with bulb C, but now it gets
all the current. So bulb B will get brighter.”
Student 2: “I don’t think so. Now there aren’t as many paths for the current, so the resistance in the circuit
has increased. Since the resistance in the circuit has gone up, the current in the circuit decreases. Bulb B will
get dimmer.”
a. Is Student 1 correct? Why or why not?
b. Is Student 2 correct? Why or why not?
c. Bulb B will [ become brighter | stay the same brightness | become dimmer ] when the wire is cut.
Explain.
19
8. The bulbs in the circuit shown to the right are identical. Assume that the battery is ideal.
a. Rank bulbs 1-6 in increasing brightness.
Explain.
b. Rank the voltages across the bulbs.
Explain.
c. Write an equation that relates the voltage across bulbs 3, 5, and 6 to the battery voltage.
9. Bulb 1 from the circuit in part 8 is removed from its socket as shown to the right.
a. The brightness of bulb 2 [ increases | remains the same | decreases ].
Explain.
b. The brightness of bulb 6 [ increases | remains the same | decreases ].
Explain.
c. The brightness of bulb 3 [ increases | remains the same | decreases ].
Explain.
20