BASIC DC CIRCUITS - Ryerson Department of Physics

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Oct 7, 2013 (4 years and 5 days ago)

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22
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1

Physics with Vernier



BASIC DC CIRCUITS

Current and voltage can be difficult to understand, because they cannot be observed directly. To
clarify these terms, some people make the comparison between electrical circuits and water flowing in
pipes. Here is a chart of the three el
ectrical units you will study in this experiment.

Electrical Quantity

Description

Unit


Water Analogy


Voltage or Potential
Difference

A measure of the Energy
difference per unit charge
between two points in a
circuit.

Volt (V)

Water Pressure

Current

A m
easure of the flow of
charge through a cross
-
section in a circuit.


Ampere (A)

Amount of water
flowing per unit time.

Resistance

A measure of how
difficult it is for current to
flow in a circuit.

Ohm (
Ω
)

A measure of how
diff
icult it is for water
to flow through a pipe.



PART I: OHM’S LAW

Georg Simon Ohm discovered the fundamental relationship among these three important electrical
quantities: current, voltage, and resistance. The relationship and the unit of electrical resi
stance were
both named for him to commemorate his contribution to physics. One statement of Ohm’s law is that
the current through a resistor is proportional to the voltage across the resistor. In this experiment you
will see if Ohm’s law is applicable to s
everal different circuits.



Figure 1


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Physics with Vernier

OBJECTIVES



Determine the mathematical relationship between current, potential difference, and
resistance in a simple circuit.



Compare the potential
vs
. current behavior of a resistor to that of a light bulb.


MATERIA
LS

computer

Vernier Circuit Board,
or

Vernier computer interface

wires

Logger
Pro


clips to hold wires

one Vernier Current Probe and

switch

one Vernier Differential Voltage Probe

resistor (about 10

Ω
)

adjustable low voltage DC power supply

light bulb
(6.3 V)


PRELIMINARY SETUP AN
D QUESTIONS

1.

Connect the Current Probe to Channel 1 and the Differential Voltage Probe to Channel
2 of the computer interface.

2.

Open the file “22 Ohms Law” in the
Physics with Vernier
folder. A table and a graph of
potent
ial
vs
. current will be displayed. The meter displays potential and current
readings.

3.

With the power supply turned off, connect the 10
Ω
resistor, wires, and clips as shown
in Figure 1. Take care that the positive lead from the power supply and the red
terminal
from the Current & Voltage Probe are connected as shown in Figure 1.
Note:
Attach
the red connectors electrically closer to the positive side of the power supply.

4.

Click
. A dialog box will appear. Click
to zero both sensors. This sets the
z
ero for both probes with no current flowing and with no voltage applied.

5.

Ask your TA to check the arrangement of the wires before proceeding. Only then,
connect the low voltage power supply, turn its control to 0

V and then turn it on.
Slowly increase t
he voltage to 3 V. Monitor the meter in bottom
-
left of the Logger
Pro

window and describe what happens to the current through the resistor as the potential
difference across the resistor increases. What happens to the current when the voltage
doubles? Defi
ne what type of relationship exists between voltage and current.

PROCEDURE

1.

Record the value of the resistance (10
Ω
) you will be using, in the first row of the data
table below.

2.

Make sure the power supply is set to 0 V. Click
to begin data collecti
on.
Monitor the voltage and current. Click
.

3.

Increase the voltage on the power supply to approximately 0.2 V. Click again
.

4.

Increase the voltage again by about 0.2 V. Click again
. Repeat this process until
you reach a voltage of 3.0 V.

5.

Click
and set the power supply back to 0 V.

6.

Are the voltage and current proportional? Click the Linear Fit button,
. Print a copy
of the graph along with the best
-
fit line and its parameters (select
Print
, then
Save As
PDF
, and save to your USB memory, with
a name of your choice).


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Physics with Vernier


7.

Replace the resistor in the circuit with a 4.5 V light bulb. Repeat Steps 2

5.

8. Click the Linear Fit button,
, and record the slope of the regression line in the data table
below.

DATA TABLE

Part I. Ohm’ Law





ANALYSIS OF RESULTS
IN PART I

1.

Compare the slope of the regression line in the first row of the table to the resistance of that
resistor.

3.

Resistance,
R
, is defined using
R
=
V/I
where
V
is the potential across a resistor, and
I
is the
current.
R
is measured in ohms (
Ω
), where 1

Ω

=

1

V/A. The constant you determined should be
similar to the resistance of that resistor. However, resistors ar
e manufactured such that their actual
value is within a tolerance. For most resistors used in this lab, the tolerance is 5% or 10%. Ask
your TA how to determine the tolerance of the resistors you are using. Calculate the range of
values for each resistor.
Does the slope of the regression line fit within the appropriate range of
values for that resistor?

4.

Does your resistor follow Ohm’s law? Base your answer on your experimental data.

5.

Does your light bulb follow Ohm’s law? Can you guess the average res
istance of the light bulb?
Base your answer on your experimental data.

PART II: VOLTAGES AN
D CURRENTS IN SERIES
AND PARALLEL
CIRCUITS

Components in an electrical circuit are in
series
when they are connected one after the other, so that
the same current f
lows through both of them. Components are in
parallel
when they are in alternate
branches of a circuit. Series and parallel circuits function differently. You may have noticed the
differences in electrical circuits you use. When using some decorative holid
ay light circuits, if one
lamp burns out, the whole string of lamps goes off. These lamps are in series. When a light bulb burns
out in your house, the other lights stay on. Household wiring is normally in parallel.




Series Circuit






Parallel Circuit

Circuit


Slope of regre
ssion line
(V/A)

Y
-
intercept of regression
line (V)

Resistor

(
Ω
)



Light bulb

(
Ω
)




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Physics with Vernier


You can monitor these circuits using a Current Probe and a Voltage Probe and see how
they operate. One goal of this experiment is to study circuits made up of two resistors in
series or parallel. You can then use Ohm’s law to determine the equivalent res
istance of the
two resistors.

OBJECTIVES



To study the current flow in series and parallel circuits.



To study the voltages across resistors in series and parallel circuits.



Use Ohm’s law to calculate equivalent resistance of series and parallel circuits.


MATERIALS

computer

Vernier Circuit Board,
or

Vernier computer interface

one 10
Ω
resistor

Logger
Pro


one 51
Ω
resistor

two Vernier Current Probes and

one 68
Ω
resistor

one Vernier Differential Voltage Probe

momentary
-
contact switch

low
-
voltage DC
power supply

connecting wires


PRELIMINARY QUESTION
S

1.

Using what you know about electricity, predict how series resistors would affect current
flow. What would you expect the effective resistance of two equal resistors in series to
be, compared to the r
esistance of a single resistor?

2.

Using what you know about electricity, predict how parallel resistors would affect
current flow. What would you expect the effective resistance of two equal resistors in
parallel to be, compared to the resistance of one a
lone?

3.

For each of the three resistor values you are using, note the
tolerance
rating. Tolerance
is a percent rating, showing how much the actual resistance could vary from the labeled
value. This value is labeled on the resistor or indicated with a colo
r code. Calculate the
range of resistance values that fall in this tolerance range.



Labeled resistor
value (
Ω
)

Tolerance (%)


Minimum
resistance (
Ω
)

Maximum
resistance (
Ω
)

10




51




68





PROCEDURE

Part II a. Voltages in Series Circuits

1.

Conn
ect the Current Probe to Channel 1 and the Differential Voltage Probe to Channel
2 of the interface.

2.

Open the file “23a Series Parallel Circ” in the “
Physics with Vernier”
folder. Current
and voltage readings will be displayed in the bottom
-
left meter
area of the window.


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Physics with Vernier


3.

Connect together the two voltage leads (red and black) of the Voltage Probe. Click
,
then click
to zero both sensors. This sets the zero for both probes with no current
flowing and with no voltage applied.

4. Connect the series
circuit shown in Figure 2 using a 10

Ω
resistor for resistor 1 and a 51
Ω

resistor for resistor 2. Notice the Voltage Probe is used to measure the voltage applied to both
resistors. The red terminal of the Current Probe should be toward the + terminal of t
he power
supply.

5.

For this part of the experiment, you do not even have to click on the
button. You can
take readings from the meter at any time. To test your circuit, briefly press on the switch to
complete the circuit. Both current and voltage readi
ngs should increase. If they do not, recheck
your circuit.










6.

Press on the switch to complete the circuit again and read the current (
I
) and total voltage
(
VTOT
). Record the values in the data table.

7.

Connect the leads of the Voltage Probe acro
ss resistor 1. Press on the switch to complete the
circuit and read this voltage (
V1
). Record this value in the data table.

8.

Connect the leads of the Voltage Probe across resistor 2. Press on the switch to complete the
circuit and read this voltage (
V2
).
Record this value in the data table.

DATA TABLE

Part II a. Voltages in Series Circuits

R
1

(
Ω
)

R
2

(
Ω
)

I

(A)

V
TOT

(V)

V
1

(V)

V
2

(V)

R
eq

(
Ω
)

10

51







ANALYSIS OF RESULTS OF PART II a.

1. What seems to be the relationship between the two voltage readi
ngs:
V
1
,
V
2
, and
V
TOT
?

2.

Using the measurements you have made above and your knowledge of Ohm’s law, calculate
the equivalent resistance (
R
eq
) of the series circuit with the two resistors you tested.


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Physics with Vernier


PART II. b: VOLTAGES IN PARALLEL CIRCUITS

1.

Connect the
parallel circuit shown below using 51
Ω
resistor for resistor 1 and 68
Ω

resistor for resistor 2. As in the previous circuit, the Voltage Probe is used to
measure the voltage applied to both resistors. The red terminal of the Current Probe
should be towar
d the + terminal of the power supply. The Current Probe is used to
measure the total current in the circuit.











Figure 3


2.

As in Part II a., you can take readings from the meter at any time. To test your
circuit, briefly press on the switch to comple
te the circuit. Both current and voltage
readings should increase. If they do not, recheck your circuit.

3.

Press the switch to complete the circuit again and read the total current (
I
) and total
voltage (
V
TOT
). Record the values in the data table.

4.

Connect t
he leads of the Voltage Probe across resistor 1. Press on the switch to
complete the circuit and read the voltage (
V
1
) across resistor 1. Record this value in
the data table.

5.

Connect the leads of the Voltage Probe across resistor 2. Press on the switch to
complete the circuit and read the voltage (
V
2
) across resistor 2. Record this value in
the data table.

DATA TABLE

Part II b. Voltages in parallel circuits

R
1

(
Ω
)

R
2

(
Ω
)

I

(A)

V
TOT

(V)

V
1

(V)

V
2

(V)

R
eq

(
Ω
)

51

68







ANALYSIS OF RESULTS OF PART II b.

1.

U
sing the measurements you have made above and your knowledge of Ohm’s law,
calculate the equivalent resistance (
R
eq
) of the parallel circuit with the resistors you tested.

2.

What seems to be the relationship between the two voltage readings
V
1
,
V
2
, and
V
TOT
in a
parallel circuit?


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Physics with Vernier



PART II c
. CURRENTS IN SERIES CIRCUITS

1.

For Part II c. of the experiment, you will use two Current Probes. Open the experiment file “23b
Series Parallel Circ.” Two graphs of current
vs.
time are displayed.

2.

Disconnect the Voltage Pro
be and, into the same channel, connect a second Current Probe.

3.

With nothing connected to either probe, click
, then click
to zero both sensors. This
adjusts the current reading to zero with no current flowing.

4.

Connect the series circuit shown in Figure
4 using the 10
Ω
and the 51
Ω
resistors. The Current
Probes will measure the current flowing into and out of the two resistors. The red terminal of each
Current Probe should be toward the + terminal of the power supply.


Figure 4


5.

For this part of the exp
eriment, you will make a graph of the current measured by each probe as a
function of time. You will start the graphs with the switch open, close the switch for a few
seconds, and then release the switch. Before you make any measurements, think about what
you
would expect the two graphs to look like. Sketch these graphs showing your prediction. Note that
the two resistors are not equal.

6.

Click on the
button, wait a second or two, then press on the switch to complete the circuit.
Release the switch just bef
ore the graph is completed.

7.

Select the region of the graph where the switch was on by dragging the cursor over it. Click on the
Statistics button,
, and record the average current in the data table. Determine the average current
in the second graph follow
ing the same procedure.

DATA TABLE

Part II c. Currents in Series Circuits



R
1

(
Ω
)

R
2

(
Ω
)

I
1

(A)

I
2

(A)

R
1
& R
2

in series

10

51





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Physics with Vernier

ANALYSIS
OF RESULTS OF PART II c.

1.

What did you discover about the current flow in a series circuit? Is that in agreement
with the expected outcome?

PART II d
. CURRENTS IN PARALLEL CIRCUITS

1.

Connect the parallel circuit as shown in Figure 5 using the 51
Ω
resistor a
nd the 68
Ω

resistor. The two Current Probes will measure the current through each resistor
individually. The red terminal of each Current Probe should be toward the + terminal of the
power supply.


Figure 5


9. Before you make any measurements, sketch yo
ur prediction of the current
vs.
time
graphs for each Current Probe in this configuration. Assume that you start with the switch
open as before, close it for several seconds, and then open it. Note that the two resistors
are not identical in this parallel
circuit.

10. Click
and wait a second or two. Then press on the switch to complete the
circuit. Release the switch just before the graph is completed.

11. Select the region of the graph where the switch was on by dragging the cursor over it.
Click the Sta
tistics button,
, and record the average current in the data table. Determine
the average current in the second graph following the same procedure.

DATA TABLE

Part II c. Currents in Parallel Circuits




R
1

(
Ω
)

R
2


(
Ω
)

I
1

(A)

I
2

(A)

R
1
& R
2

in parallel

51

68




ANALYSIS OF RESULTS OF PART II d.

1.

What did you discover about the current flow in a parallel circuit?

2.

If the two measured currents in
your parallel circuit were not the same, which resistor had
the larger current going through it? Why?