In the first laboratory of this quarter, we learned about
static electric fields and the deflection of a beam of electrons
by an electric field in the cathode ray tube (CRT). This beam of
electrons is one example of an **electric current** -- charges
in motion. The current in the CRT was unique in that the motion
of the electrons could be completely determined by simple
kinematics.

In contrast to the CRT, most of the electric currents you are familiar with flow inside a material, like wires or light bulbs, and are not predictable by simple kinematics. A detailed understanding of electric current is quite complicated since the electrons interact in a very special way with the atoms that make up the material. A simple model is to imagine yourself trying to get through a narrow hall crowded with students waiting to get to their class and not getting out of your way. Trying to model or describe your interactions with these people and how you actually get through this mob of students is an incredibly difficult task.

Fortunately, several simple laws describe the macroscopic behavior of electric currents in most materials. The purpose of this lab is to allow you to transfer your knowledge of electricity from the highly ideal situation of currents in a vacuum to the everyday case of currents in materials. This will allow you to master the basics of "circuit analysis" that are crucial to understanding much of today's technology from hooking up your VCR to computer circuitry.

**OBJECTIVES:** After successfully completing this
laboratory, you should be able to:

- relate the electric current in a circuit to the
resistance and voltage in the circuit;

- apply the junction and loop laws to determine the current
in a simple circuit;

- measure the current through a circuit element with a
Digital Multimeter (DMM);

- measure the voltage between two points in a circuit with
a DMM; and

- measure the resistance of a circuit element, both with a
DMM and by using the definition of resistance.

**PREPARATION:**

Read Fishbane, Gasiorowicz, and Thornton: Chapter 27, sections 1, 3 and 7; Chapter 28, sections 1 through 4. You may be reading this material for lab before you need it for lecture. If so, it is even more important that you read the material before coming to lab.

**EXPLORATORY PROBLEM #1: SIMPLE CIRCUITS**

You and your friend are trying to solve a homework problem. The problem involves comparing the current through identical resistors in simple one-resistor and two-resistor circuits with identical batteries. Your friend believes that if the resistors were actually identical light bulbs, then they would all glow with the same brightness because the batteries are identical (see diagram below). Do you agree with your friend? To resolve the issue, you decide to build the circuits shown below and observe the brightness of the bulbs.

How does the brightness of the bulbs compare in
simple one-bulb and two-bulb circuits? |

**EQUIPMENT**

You will build the three simple circuits shown below out of wires, bulbs, and batteries. Use the accompanying legend to help you build the circuits. |

**PREDICTION**

Rank order the brightness of bulbs A, B, C, D, and E from the
brightest to the dimmest (use the symbol **=** for "same
brightness as" and the symbol **>** for "brighter
than"). Explain your reasoning. Is your prediction different
from your friend's prediction?

**EXPLORATION**

**Reference Circuit**: Connect Circuit I to use as a
reference.

**Series Circuit:** Connect Circuit II. Compare the
brightness of bulbs B and C. What can you conclude from this
observation about the amount of current through each bulb? Note:
Pay attention to large differences you may observe, rather than
minor differences that may occur if two "identical"
bulbs are, in fact, not identical. How can you test whether minor
differences are due to manufacturing irregularities?

Is current "used up" in the first bulb, or is the current the same through both bulbs? Based on your observation, what can you infer about the current at points 1, 2, and 3?

How does the brightness of bulb A (Circuit I) compare to the brightness of bulbs B and C (Circuit II)? What can you infer about the current at point 1 in the two circuits?

**Parallel Circuit: **Connect Circuit III. Compare the
brightness of bulbs D and E. What can you conclude from this
observation about the amount of current through each bulb?

Describe the flow of current around the entire circuit. What do your observations suggest about the way the current through the battery divides and recombines at junctions where the circuit splits into two parallel branches? How does the current at point 1 compare with the currents at points 2 and 3?

How does the brightness of bulb A (Circuit I) compare to the brightness of bulbs D and E (Circuit II)? What can you infer about the current at point 1 in the two circuits?

Comparing the three circuits, does the amount of current at point 1 appear to remain constant or to depend on the number of bulbs and how they are connected?

**CONCLUSION**

Rank order the actual brightness of the bulbs. How did this compare to your prediction? Was your friend right about how the brightness of the bulbs compare in simple one-bulb and two-bulb circuits?

Can you use the conservation of energy and the conservation of charge to explain your results? Does a battery supply a constant current or a constant "voltage" (potential difference) to circuits?

**Check
Your Understanding:**

Rank order the brightness of the bulbs in the following circuits:

**EXPLORATORY PROBLEM #2: MORE COMPLEX CIRCUITS**

You and your friend are still solving homework problems about circuits. Your strategy for Problem 1 was so successful that you decide to build slightly more complex circuits and observe and compare the brightness of the bulbs.

How does the brightness of the bulbs compare in these
more complex circuits? |

**EQUIPMENT**

You will build the three simple circuits shown below out of wires, bulbs, and batteries. Use the accompanying legend to help you build the circuits. |

**PREDICTION**

Rank order the brightness of the bulbs A, B, C, D, E, F, and G
from the brightest to the dimmest (use the symbol **=** for
"same brightness as" and the symbol **>** for
"brighter than"). Explain your reasoning.

**EXPLORATION**

**Reference Circuit**: Connect Circuit I to use as a
reference.

**Circuit IV:** Connect Circuit IV. Compare the brightness
of bulbs B and C. Compare the brightness of bulbs B and C to bulb
D. What can you conclude from this observation about the amount
of current through each bulb? [Note: Pay attention to large
differences you may observe, rather than minor differences that
may occur if two "identical" bulbs are, in fact, not
identical. How can you test whether minor differences are due to
manufacturing irregularities?]

How does the brightness of bulbs B and C compare to the brightness of bulb A (Circuit I)? What can you infer about the current at point 2 in Circuit IV and the current at point 1 in Circuit I?

How does the brightness of bulb D compare to the brightness of bulb A (Circuit I)? What can you infer about the current at point 3 in Circuit IV and the current at point 1 in Circuit I?

Describe the flow of current around the entire circuit. What do your observations suggest about the way the current through the battery divides and recombines at junctions where the circuit splits into two parallel branches? How does the current at point 1 compare with the currents at points 3 and 4?

**Circuit V:** Connect Circuit V. Compare the brightness of
bulbs F and G. Compare the brightness of bulbs F and G to bulb E.
What can you conclude from this observation about the amount of
current through each bulb? [Note: Pay attention to large
differences you may observe, rather than minor differences that
may occur if two "identical" bulbs are, in fact, not
identical. How can you test whether minor differences are due to
manufacturing irregularities?]

How does the brightness of bulb E compare to the brightness of bulb A (Circuit I)? What can you infer about the current at point 1 in Circuit V and the current at point 1 in Circuit I?

How does the brightness of bulb E compare to the brightness of bulb B (Circuit IV)? You can switch between Circuit IV and Circuit V quickly by switching the wire connected to the top of bulb G to the top terminal of bulb E. Watch the brightness of bulb E while you do this.

Describe the flow of current around the entire circuit. What do your observations suggest about the way the current through the battery divides and recombines at junctions where the circuit splits into two parallel branches? How does the current at point 2 compare with the currents at points 3 and 4?

**CONCLUSION**

Rank order the actual brightness of the bulbs A, B, C, D, E, F, and G. How did your prediction compare to your results? Can you use the conservation of energy and the conservation of charge to explain your results?

**PROBLEM #3: RESISTORS AND LIGHT BULBS**

You are helping your former high school physics teacher sort through some equipment to help out the junior high science fair. You are looking for two resistors. You find one old, color-coded resistor and a light bulb that you think might work. You would like the resistors to be "ohmic." That is, when you double the voltage across the resistor, you double the current. Will your resistor and light bulb work?

Are the color-coded resistor and light bulb ohmic
resistors? If so, what are their resistances? |

**EQUIPMENT**

You will have wires, a power supply, a digital Multimeter (DMM), a light bulb, and a " mystery" resistor. In this experiment, you will vary the voltage across the color-coded resistor or light bulb with the power supply and measure the resulting current.

**PREDICTIONS**

Draw a sketch of what you expect a graph of voltage versus current to look like for (a) the standard resistor, and (b) the light bulb. Explain your reasoning

**METHOD QUESTIONS**

**1.** Sketch what you expect the graph of voltage versus
current to look like if the resistor is made of ohmic material.
How is the slope of the graph related to its resistance?

**2.** Given the fact that as a light bulb gets brighter,
it gets hotter, how do you expect its resistance to depend on its
brightness? [Hint: refer to Chapter 27 in your text.]

Sketch what you would expect the graph of voltage versus current to look like for the light bulb.

**EXPLORATION**

WARNING: You will be working with a power supply that
can generate large electric voltages. Improper use can
cause painful burns. To avoid danger, the power should be
turned OFF and you should WAIT at least one minute before
any wires are disconnected from or connected to the power
supply. |

Sketch the circuit you will build to answer your prediction. Can you test both the light bulb and the resistor at the same time? Is this a good idea?

Read Appendix A and get familiar with the different operations of the digital Multimeter (DMM).

**MEASUREMENT**

There are three methods for determining the electrical
resistance of a **resistor**:

1. Use the chart provided in the laboratory (and also in Appendix A) to determine the resistance of your resistor based on its color code. What is the uncertainty in this value?

2. Use the DMM to measure the resistance of the resistor. What is the uncertainty in this value?

3. Use your power supply, DMM, and resistor to measure the voltage across the resistor and the current through the resistor for several different voltages. What is the uncertainty in the value of the resistance obtained by this method?

Use the second and third methods above to determine the
resistance of your **light bulb**.

**ANALYSIS**

Make a graph of voltage versus current for your resistor and light bulb. How do the values of the resistances compare for the different methods used? Which do you think is the most accurate? Why?

**CONCLUSION**

Are the color-coded resistor and light bulb ohmic resistors? If so, what are their resistances? Did your prediction match your results? If not, why? Explain your reasoning.

**PROBLEM #4: CIRCUIT ANALYSIS (PART A)**

You are applying for a summer job at an electronics company that pays $15 per hour with benefits. As part of the interview process, the plant manager gives you two simple circuits and asks you to determine the current flowing through each resistor in the circuits. If you can tell her, you get the job. This first circuit problem is essentially problem 28-15 in your textbook.

What is the current flowing through each resistor in
the circuit shown below? |

**EQUIPMENT**

You will build a simple circuit (Circuit VI shown at right) out of wires, resistors, and batteries or a power supply. You will, of course, have a digital Multimeter (DMM) for measuring resistances, voltages, and currents. |

**PREDICTION**

Predict quantitatively the current through each resistor of Circuit VI.

**METHOD QUESTIONS**

It is useful to follow an organized problem-solving technique, like the one on page 822 of your text:

**1.** Draw a diagram showing sources of voltages and
resistors. Label your diagram. Sometimes you may need to redraw
the given circuit to help yourself see which resistors are in
series and which are in parallel. For this lab, the voltages and
the resistors are the known quantities and the current in each
resistor is the unknown.

**2.** Assign a separate current for each leg of the
circuit, and indicate that current on the diagram.

**3**. Apply the junction rule (Equation 28-12, page 820)
for the currents at each junction.

**4**. Identify the number of loops by counting the number
of closed circuit paths and label them on the diagram. Apply the
loop rule (Equation 28-9, page 818) to each of these loops.

**5**. Check that the number of linear equations from
Method Questions 3 and 4 matches the number of unknowns.

Solve your equations for one of the unknown currents and express the other currents in terms of the first current. You can now complete your prediction.

**EXPLORATION**

If you have not used the digital Multimeter (DMM), read Appendix A and get familiar with the different operations of the DMM.

Build Circuit VI. How do you know that there is current flowing through the circuit? How do the currents at each junction relate? What is the resistance of each resistor? What is the potential difference provided by the batteries? How can you find the answers to these questions?

Complete your measurement plan.

**MEASUREMENT**

Measure the resistances, the currents flowing through each resistor, and the potential difference provided by each battery.

**ANALYSIS**

Calculate the current through each resistor using your Prediction equations and your measured values of the resistances and potential difference provided by each battery.

**CONCLUSION**

Did your measured and predicted values of the currents through the resistors agree? If so, you got the job. If not, explain the discrepancy.

**PROBLEM #5: CIRCUIT ANALYSIS (PART B)**

You are working on your interview questions for the summer job that pays $15 per hour with benefits. This is the second of the two circuits for which you were asked to find the current flowing through each resistor. If you can, you get the job. This circuit problem is essentially problem 28-16 in your text book

What is the current flowing through each resistor in
the circuit shown below? |

**EQUIPMENT**

You will build a simple circuit (Circuit VII shown at right) out of wires, resistors, and batteries or a power supply. You will, of course, have a digital Multimeter (DMM) for measuring resistances, voltages, and currents. |

**PREDICTION**

Predict quantitatively the current through each resistor of Circuit VII?

**METHOD QUESTIONS**

It is useful to follow an organized problem-solving technique, like the one on page 822 of your text:

**1.** Draw a diagram showing sources of voltages and
resistors. Label your diagram. Sometimes you may need to redraw
the given circuit to help yourself see which resistors are in
series and which are in parallel. For this lab, the voltages and
the resistors are the known quantities and the current in each
resistor is the unknown.

**2.** Assign a separate current for each leg of the
circuit, and indicate that current on the diagram.

**3**. Apply the junction rule (Equation 28-12, page 820)
for the currents at each junction.

**4**. Identify the number of loops by counting the number
of closed circuit paths and label them on the diagram. Apply the
loop rule (Equation 28-9, page 818) to each of these loops.

**5**. Check that the number of linear equations from
Method Questions 3 and 4 matches the number of unknowns.

Solve your equations for one of the unknown currents and express the other currents in terms of the first current. You can now complete your prediction.

**EXPLORATION**

If you have not used the digital Multimeter (DMM), read Appendix A and get familiar with the different operations of the DMM.

Build Circuit VI. How do you know that there is current flowing through the circuit? How do the currents at each junction relate? What is the resistance of each resistor? What is the potential difference provided by the batteries? How can you find the answers to these questions?

Complete your measurement plan.

**MEASUREMENT**

Measure the resistances, the currents flowing through each resistor, and the potential difference provided by each battery.

**ANALYSIS**

Calculate the current through each resistor using your Prediction equations and your measured values of the resistances and potential difference provided by each battery.

**CONCLUSION**

Did your measured and predicted values of the currents through the resistors agree? If so, you got the job. If not, explain the discrepancy.

**PROBLEM #6: WHEN TO USE QUANTITATIVE RULES**

You have a summer job in an electronics company that requires you to make quick judgments about the relative amounts of current in through different resistances in complex circuits. You have been tediously using Kirchhoff's rules to find the current through each resistance.

Your boss says you have been taking too much time. She gives
you four **qualitative** rules (see the Method Questions) and
the circuits shown below to practice using the rules.

How will the brightness of the bulbs compare in the
three complex circuits? |

**EQUIPMENT**

You will have batteries, wires, and five identical bulbs you can connect in the three circuits shown below.

**PREDICTIONS**

1. Use the qualitative rules given in the Methods QuestionsSection to complete the following predictions. For each prediction, state which rule(s) you used.

__Circuit VIII:__

- How will the brightness of bulb A compare with the
brightness of bulb B?

- How will the brightness of bulb A compare with the
brightness of bulb D?

- How will the brightness of bulb B compare with the
brightness of bulb D?

__Circuit IX:__

- How will the brightness of bulb A compare with the
brightness of bulb B?

- How will the brightness of bulb B compare with the
brightness of bulb C?

- How will the brightness of bulb B compare with the
brightness of bulb D?

__Circuit X:__

- How will the brightness of bulb A compare with the
brightness of bulb B?

- How will the brightness of bulb B compare with the
brightness of bulb C?

- How will the brightness of bulb B compare with the
brightness of bulb D?

2. Of course, sometimes it is necessary to do some quick calculations. Use the equations for finding equivalent resistances (see pages 819 and 823) as well as the qualitative rules to predict the relative brightness of bulb A in the three circuits.

**METHOD QUESTIONS**

In completing your predictions, use the following **qualitative**
rules:

**1.** Resistances in series have the same current flowing
through each. Resistances in series add, so the current through a
path decreases as the total resistance of the path increases.

**2.** Current divides at a junction. The current through
each path depends on the resistance of the path -- the larger the
resistance, the smaller the current. Paths of equal resistance
will have the same current.

**3.** Resistors in parallel offer less total resistance
than the smallest resistance in the configuration.

**4.** Parallel branches connected directly across a
battery are independent -- each set of parallel branches has the
same voltage drop as if it were the only connection to the
battery.

**EXPLORATION AND MEASUREMENT**

Set up each circuit one at a time and observe the actual brightness of the bulbs. How can you test whether minor differences you observe are due to manufacturing irregularities in the "identical" bulbs?

Coordinate with other groups to compare the brightness of bulb A in the three circuits. How can you test whether minor differences you observe are due to manufacturing irregularities in the "identical" bulbs?

If needed, use a DMM to measure the current through bulb A in the three circuits (see Appendix A ).

**ANALYSIS AND CONCLUSION**

Explain any differences between your predictions and your observations.

Each qualitative rule is the result of applying the conservation of energy (Kirchhoff's loop rule) and the conservation of charge (Kirchhoff's junction rule) to series and/or parallel configurations. For each qualitative rule, write the equation(s) that correspond to each rule.

**EXPLORATORY PROBLEM #7: SHORT CIRCUITS**

The purpose of this problem is to help you learn what short circuits are and how to avoid them.

What is a short circuit? |

**EQUIPMENT**

You will build the three simple circuits shown below out of wires, bulbs, and batteries. Use the accompanying legend to help you build the circuits. | |

**PREDICTIONS**

Circuit I: What happens to the brightness of the bulb A when a wire is attached across the bulb?

Circuit II: What happens to the brightness of bulbs B and C when a wire is attached across bulb B?

Circuit III: What happens to the brightness of bulbs D and E when a wire is attached across bulb E?

**EXPLORATION**

WARNING: A short circuit is what happens any time a
very low-resistance path (like a wire, or other piece of
metal) is provided between points in a circuit that are
at voltages, like the terminals of a battery or power
supply. Short circuits can destroy equipment and injure
people! Short circuits damage equipment by creating large
currents in a circuit that is not designed for large
currents. These currents can cause great heat and cause
damage to nearby circuit elements or measuring devices.
Any short circuits suggested in this manual have been
tested, and determined not to significantly damage the
equipment. |

Build Circuit I. Place a wire across the bulb. What happens to the brightness of the bulb? Hold on to the wire that is across the bulb. Is it getting warmer? Disconnect the battery. Placing the wire across the bulb causes a short circuit and it is called "shorting out" the bulb.

Build Circuit II. What happens to the brightness of bulbs B and C when you place a wire across bulb B? What is the value of the current at point 2? Is the wire across bulb B getting warm? Explain your answers.

Build Circuit III. What happens to the brightness of bulbs D and E when you place a wire across bulb E? What is the value of the current at point 2? At point 3? Is the wire across bulb E getting warm? Explain your answers.

**CONCLUSION**

Did your predictions match your observed results? Explain your answers.

**Check
Your Understanding:**

1. What would happen to the brightness of bulb A in the circuit below if more bulbs were added parallel to bulbs B and C?

In household circuits, bulb A is in the same position as a fuse or circuit breaker. Why?

2. Rank order Circuits I through IV from the largest current at point 1 to the smallest current at point 1. Explain your reasoning.

3. Predict what will happen to the brightness of bulbs A, B, C and D if bulb E were removed from its socket. Explain your reasoning. |

4. For the circuit below, determine the currents in each resistor.

This is the same circuit as problem 28-26.

5. For the circuit below, determine the value for R such that the current I3 is 0.1A with the indicated direction. This is problem 28-29.

What is the value for R that will give a current I3 = 0.1 A, but in the opposite direction as what is shown?