D.C. Circuits Objectives Introduction Theory

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DC 1
DC1

D.C. Circuits

Objectives

1. To gain experience in building D.C. circuits, and making measurements of
current and voltage.

2. To strengthen the ability to reason about how adding or removing resistors will
affect the current and potential at different locations in a D.C. circuit.

Introduction

This tutorial/lab is designed to review, solidify, and improve your understanding of D.C.
circuits and Ohm’s law. Research has shown that even after students have completed
their study of D.C. circuits, they often have difficulty with some specific concepts and
ideas. The exercises here are designed to address these difficulties in a step by step
fashion, and help you learn to reason more easily and correctly about circuits.

In each part of the lab, you will be given a circuit diagram, involving a power supply
(constant voltage), and a number of small light bulbs. You will be asked to make some
predictions about the behaviour of the circuit before you actually construct the circuit and
make any necessary measurements. No quantitative calculations are required.
Hopefully some of the circuits will surprise you with their behaviour!

Theory

The flow of electric charge through a wire and around a circuit is called electric current,
or simply current. This current is a measure of how many coulombs of charge pass by
a given point of the circuit each second. Its unit is ampere (SI symbol is A).

1 ampere = 1 coulomb/second or 1 A = 1 C/s . (1)

An electromotive force (emf) or a voltage ΔV causes the charge to move around the
circuit (similar to water pressure pushing water through a hose). Its unit is volt (V).

The resistance is a measure of a material’s ability to restrict the amount of charge from
flowing through it. In a wire of low resistance, the electrons will flow relatively easily.
The unit for resistance is ohm (Ω).

Conventional current is in the opposite direction to electron flow. In a solid conductor,
there is no flow of electric charge in the direction of conventional current, but in a fluid

(liquid or gas), both negative charge (negative ions and electrons) and positive charge
can move so, in practice, there is no disadvantage to having electric current defined in
the direction that positive charge flows.
DC 2

Ohm’s law is the relationship among voltage (ΔV), current (I) and resistance (R):

ΔV = IR (2)

The single resistor that is equivalent to n resistors in series is:

R
S
= R
1
+ R
2
+ ... + R
n
(3)

The single resistor that is equivalent to n resistors in parallel is:

R
P
-1
= R
1
-1
+ R
2
-1
+ ... + R
n
-1
(4)


A resistor is represented by the symbol

a connecting lead or wire by

and a battery or power supply by


An ammeter is a device for measuring current (
). It has almost no
resistance and is placed in the circuit, so that the current to be measured will pass
through it. Do NOT
connect an ammeter in parallel with the resistor. It will smoke!



Figure 1. Connecting an ammeter in a circuit.

A voltmeter (
) measures voltage. It has a high resistance and is placed
in parallel to, or “across”, the voltage to be measured. An ideal voltmeter has infinite
resistance, so I
V
= 0 in Figure 2 if the voltmeter is ideal.

DC 3


Figure 2. Connecting a voltmeter in a circuit.


In this lab, a light bulb will be represented the following symbol:

The brightness of a bulb is measured by the power it dissipates:

Power = Current x Voltage = I ΔV (5)

The main advantage to using light bulbs in the circuits is that we can usually see what is
happening as soon as we make a change to the circuit. Also, we can generally assume
all the bulbs will be the same brightness under the same conditions, without needing to
carefully measure their resistance. The major disadvantage to real light bulbs is that
their resistance varies strongly with the current through them. This means that the
circuits in the lab will not always behave the same way as we would expect for ideal light
bulbs with constant R. It is important to keep this in mind when you observe the circuits.
In some ways it may not even be a disadvantage that this happens, because it is a
common problem all experimenters must confront: most real equipment doesn’t behave
like the ideal assumed in textbooks. The models we build in physics usually assume
perfect voltmeters, ammeters, and light bulbs. If you can reason correctly about the
ideal case, and then extend that to account for the non-ideal real world, your
understanding is probably much greater than if you were blindly unaware of possible
complications. Another small drawback to note about the light bulbs is that when there
is only a small voltage across them (around 0.50 V or less), they will not appear to be lit.
This is easily checked, though, by either measuring the voltage across the bulb, or the
current through it, or by simply unscrewing the bulb and seeing if that affects the rest of
the bulbs in the circuit. If it does, you know there was current through the bulb.

Apparatus

DC power supply (0 – 20 V), 4 small light bulbs in sockets, digital meter, 2 switches,
electrical leads.

Procedure

1. Set up the power supply and basic circuit.

CAUTION: The bulbs in this lab are easily blown if the voltage across them exceeds
several volts. Please be very careful to follow the instructions below concerning
how to use the power supply appropriately for this experiment. Also, in order to
DC 4
preserve the life of the bulbs, please open the switches and disconnect a wire from
the power supply whenever you are not making measurements on the circuit. (This
is preferable to turning off the power supply or turning down the voltage settings on
the power supply.) Finally, when the meter is used as an ammeter to measure
current, it has a very small resistance and could be damaged if it is placed incorrectly
in the circuit. Always double check your circuit before closing the switches and
turning on the meter, and if you are not certain it is correct, ask your lab instructor.


Figure 1 The power supply.

Figure 1 is a drawing of the power supply. In this
lab, we will be using the power supply as a
constant voltage source.

With the power supply off and the switch open,
set up Circuit 1. The fine and coarse voltage dials
should be turned down (CCW) as far as they will go.
The current dial can be turned up (CW) until the
white dot is at the top, as shown Figure 1. Turn on
the meter to read D.C. volts. Turn on the power
supply – only the green light should be on. Carefully turn up the voltage dials until
the voltmeter reads in the range 2.00 V − 2.04 V. Leave the voltage settings as
they are now until experiment 5. The green light should be on and the red light
should not be on now or for any of the measurements you make. (When the red
light is on, it means that the power supply is limiting the current it outputs, and it does
this by reducing the voltage. In this lab, we want to ensure that the voltage output is
reasonably constant at 2.0 V.)
Δ
V
a
b
Circuit 1
V
A

XANTREX LABORATORY POWER SUPPLY
D.C. VOLTS
D.C. AMPERES
2 V
FINE
COARSE
MODE
VOLTAGE
CURRENT
+
ON
OFF
This red light
should be off
This green
light should
be on
Do not use
Use these
outputs for
your circuits
DC 5
Close the switch. The voltage out of the power supply will drop slightly, but remain
close to 2.00 V, and the bulb should light.

Experiment 1 : Current at different places in a circuit


Disconnect the voltmeter from Circuit 1. Before making any measurements, make a
prediction comparing the current at the point a in Circuit A to the current at the point
b, when the switch is closed. Is I
a
greater than, less than, or equal to I
b
? Explain
briefly. Discuss any differences in the prediction with your lab partner, and try to
convince him/her that you are right.

Use the meter as an ammeter (2 A setting) to measure the current at a and b. (Keep
in mind that the resistance of the bulbs changes as they warm up, so the ammeter
values change slowly with time. Be patient.) Report your results and conclusions.
(Remember that the digital meter is not exact!) If your prediction was not correct, try
carefully to identify any mistakes in your reasoning.

At this point, it would be a good idea to check each of your light bulbs, one at a time,
in Circuit 1. Replace any burnt out bulbs. Note that there are usually differences in
brightness among the bulbs, and you may observe significantly different current
values when you change bulbs. (What causes these differences?)

2. Resistors in series.

Circuit 2 shows two light bulbs in series. Assume
that the power supply has ΔV = 2.0 V, the same as
in Circuit 1, and bulbs A and B have equal
resistance. Before you construct the circuit, write
brief answers to the following questions.

After the switch is closed in Circuit 2:

a) How will the brightness of the bulbs A and B
compare to each other, and to the brightness of
bulb A in circuit 1? Explain your reasoning briefly.

(b) Rank the currents at a, c, and d in Circuit 2.

(c) What will be the values of the voltage across the closed switch (ΔV
ab
), the
voltage across bulb A (ΔV
bc
), and the voltage across bulb B (ΔV
cd
)? Explain briefly.

(d) What happens to the brightness of bulb A if bulb B is unscrewed? Explain
briefly,

(e) With bulb B screwed back in, what will happen to the brightness of A and B if you
connect a wire between points c and d? Explain carefully.
Δ
V
a

Circuit 2
c
A
B
d
DC 6
Experiment 2a : Resistors in Series


Making no changes to the settings on the power supply, construct Circuit 2. Check
that the voltage across the power is supply is the same as it was before. Adjust it if
necessary, and then close the switch. Describe the brightness of the bulbs.

Measure the voltage across the switch, and across each bulb. Measure the current
at a, c, and d in the circuit. (Notice that the current is not half the current in circuit 1,
as it would be if these were ideal bulbs whose resistance never changed.)

With the switch closed, try unscrewing bulb B. What happens?

After bulb B is screwed back in, close the switch and then connect a wire between c
and d and describe how the brightness of bulbs A and B change. Measure the
voltage across each of the bulbs with the wire in place.

Write a brief conclusion to experiment 2a, describing the current, voltage, and other
characteristics of a series circuit.

Experiment 2b: Resistors in Series with an open switch


Refer to the original circuit 2, with the switch open. Predict the values of the voltage
across the open switch (ΔV
ab
), the voltage across bulb A (ΔV
bc
), and the voltage
across bulb B (ΔV
cd
). Explain your prediction carefully.

Measure the voltages in the circuit when the switch is open (there should no longer
be a connecting wire between points b and c).

Write a brief conclusion to experiment 2b, describing the current, voltage, and other
characteristics of a series circuit with an open switch.

Experiment 2c: Three Resistors in Series


Predict how the brightness of bulbs A and B will change if you add a third bulb in
series to circuit 2. Does it make a difference where in the circuit (before A, between
A and B, after B) you add the third bulb?

Add a third bulb to the circuit and check your predictions.








DC 7
3. Resistors in Parallel

Circuit 3 shows two light bulbs in parallel.
Assume that the power supply has
ΔV = 2.0 V, the same as in Circuit 1. Before
you construct the circuit, write brief answers to
the following questions.

a) Suppose only switch S1 is closed. How will
the brightness’s of the bulbs A and B compare
to the brightness of bulb A in circuit 1? How will the brightness’s of A and B change
when S2 is also closed? Explain your reasoning briefly.

After both switches are closed in Circuit 3:

(b) Rank the currents at a, b, and c in Circuit 3. Explain briefly.

(c) What will be the values of the voltage across bulb A (ΔV
ac
), and the voltage
across bulb B (ΔV
bc
)? Explain briefly.

(d) What happens to the brightness of bulb A if bulb B is unscrewed? Explain
briefly.

(e) With bulb B screwed back in, what will happen to the brightness of A and B if you
connect a wire between points a and c? Explain carefully, and PLEASE DO NOT
TRY THIS!

Experiment 3 : Resistors in Parallel


Making no changes to the settings on the power supply, construct Circuit 3. Check
that the voltage across the power is supply is the same as it was before. Adjust it if
necessary.

Close S1 and observe how the brightness’s of the two bulbs change after you close
S2. Measure the voltage across each bulb, and the current at a, b, and c in the
circuit.

Try unscrewing bulb B. What happens?

Write a brief conclusion to experiment 3, describing the current, voltage, and other
characteristics of a parallel circuit.



B
A
Δ
V
Circuit 3
b
a
c
S1
S2
DC 8
4. Resistors in Series and Parallel

Refer to Circuit 4. Assume that the power supply
has ΔV = 2.0 V, the same as in Circuit 1. Before
you construct the circuit, write brief answers to the
following questions.

After both switches are closed in Circuit 4:

a) Rank the three bulbs according to their
brightness. Explain your reasoning briefly.

(b) Rank the currents at a, b, c, d, and e. Explain
briefly.

(c) What happens to the brightness’s of bulbs A and C if bulb B is unscrewed?
Explain briefly.

(d) With bulb B unscrewed, what is the voltage across bulb A? bulb B? bulb C?


Experiment 4 : Resistors in Series and Parallel


Making no changes to the settings on the power supply, construct Circuit 4. Check
that the voltage across the power is supply is the same as it was before. Adjust it if
necessary.

Close the switches and observe and record the relative brightness of the three bulbs.
Measure the voltage across each bulb, and the current in each branch of the circuit.

Try unscrewing bulb B. What happens? Measure the voltage across the bulbs after
B is unscrewed.

Write a brief conclusion describing the current and voltage in the various branches of
Circuit 4. What can you conclude about an open switch or unscrewed bulb in one
branch of a parallel circuit?

5. More Resistors in Series and Parallel

Refer to Circuit 5. Assume that the power supply has ΔV = 4.0 V, double the
voltage in Circuit 1. Also assume that all the bulbs have the same resistance.
Before you construct the circuit, rank the four bulbs according to their brightness
after the switch is closed. Explain your reasoning briefly.



A
Δ
V
C


c
匱S


d

Circuit 4
DC 9
Δ
V
Circuit 5
A
B
C
D
Δ
V
Circuit 6
A
B
C
G
D
E
F
Experiment 5a : Resistors in Series and Parallel as in Circuit 5


Construct Circuit 5. With the switch open, and using
the voltmeter, increase the voltage across the
power is supply to 4.0 V.

Close the switch and observe and record the
relative brightness of the four bulbs.

Measure the current as it leaves the power supply.

Were your predictions about the circuit correct? If not, try carefully to identify any
mistakes in your reasoning.

Now refer to Circuit 6. Assume
that the power supply has ΔV =
4.0 V, the same as the voltage
in Circuit 5. Before you
construct the circuit, and after
the switch is closed, answer the
following questions.

(a) How does the total current out of the power supply in Circuit 6 compare to that of
Circuit 5? Explain your reasoning.

(b) How does the current through bulb C compare to the current through D and E?

(c) Rank the seven bulbs according to their brightness after the switch is closed.
Explain your reasoning briefly.

Experiment 5b : Resistors in Series and Parallel as in Circuit 6


Working together with another group, so that you have enough bulbs, set up circuit 6.
Before closing the switch, use the voltmeter to check that the voltage across the
power supply is 4.0 V.

Record the relative brightness of the bulbs. (Keep in mind that not all these bulbs
have exactly the same resistance, so two bulbs in series may not always look equally
bright. If you are unsure if a bulb is lit or not, try unscrewing it or breaking its
connection to the circuit. )

Measure the current as it leaves the power supply. How does it compare to Circuit
5? (Again, keep in mind that all the real bulbs are not exactly identical.)

Were your predictions about the circuit correct? If not, try carefully to identify any
mistakes in your reasoning.
DC 10
Question

Consider the following circuits, each containing an identical constant voltage power
supply, resistor, and light bulb. Assume that the meters are ideal.

(a) In which circuit does the voltmeter correctly read the voltage across the bulb? Why?

(b) In which circuit does the ammeter correctly read the current through the bulb? Why?

(c) Rank the circuits according to the brightness of the bulb. Explain your reasoning
clearly.



ΔV
Circuit A
Bulb
Resistor
Δ
V
Circuit B
V
Bulb
Resistor
ΔV
Circuit C
Bulb
Resistor
A
Δ
V
Circuit D
Bulb
Resistor
V
ΔV
Circuit E
V
Bulb
Resistor
Δ
V
Circuit F
A
Bulb
Resistor