Download PHY 124 Lab 3

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PHY 124 Lab 3 - DC circuits
Important! You need to print out the 2 page worksheet you find by clicking on this link and bring it with
you to your lab session. [http://www.ic.sunysb.edu/Class/phy122pk/labs/pdfs/Phy124Fall2011Lab3worksheet.pdf]
If you need the .pdf version of these instructions you can get them here
[http://www.ic.sunysb.edu/Class/phy122pk/labs/pdfs/Phy124Fall2011Lab3.pdf].
Goals
The purpose of this laboratory is to observe the relationship between voltage drop across (not through),
and current through (not across), electrical circuit elements. You will also gain familiarity with connecting
circuits and with voltmeters (measuring voltage across a circuit element or elements-in-parallel) and
ammeters (measuring current through a circuit element or elements-in-series). To help you in doing this
laboratory, you should review the material in Chap. 22, Current and Resistance, and Chap. 23, Circuits, of
KJF2: Knight, Jones, and Field, College Physics: A Strategic Approach, 2nd ed., the textbook for the
course.
Video
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Equipment
■ 1 DC Power Supply
■ 1 Voltmeter (yours may be different from the picture; use the DC volts setting)
■ 1 Ammeter (yours may be different from the picture; use the DC amps setting)
■ 1 board with resistive components
■ 7 test leads (wires) with banana plugs
■ 4 “alligator clip” clamps with banana sockets
Figure 1 is just below here
Introduction
Ohmic components obey Ohm's law,
V = IR (3.1)
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where V is voltage and I is current through a resistor with resistance R. Ohmic components will keep a
constant resistance with varying voltage and current. This can be seen as a linear relationship on a V vs. I
graph or an I vs. V graph. (Both kinds are commonly used.) Standard circuit resistors are ohmic. Other
kinds of electrical components may not be and in these R may depend on factors such as the temperature
(as it does in light bulbs), the direction of current flow (for example in diodes), or the light intensity falling
on the component (light sensitive diodes).
You will use a voltmeter to measure V, the voltage drop across the component, and an ammeter to
measure I, the current flow through the component. You must keep in mind that ammeters must be
connected in series in circuits, while voltmeters must be connected in parallel across the circuit component
whose voltage drop is to be measured. The figure below shows the proper setup.
Figure 2 is just above here
Technical note: non-zero meter readings are obtained only when some current flows through the meters.
Hence, the meters have two connections. The current flowing through the meters influences the
measurement. You want this effect to be very small. Thus “good” voltmeters have a large resistance
compared to R, which allows only a small current to pass through. Since the voltmeter is in parallel to the
resistor, the current through R is essentially determined by R and only a very small current flows through
the voltmeter. The equivalent resistance of R and the voltmeter in parallel is close to the resistance of R
1
because if Rvoltmeter »R then R 1
+ 1R
R . The voltmeter you use has the desired property i.e. it’s
voltmeter
resistance is much larger than the resistance to be measured, R.
In an ideal case a “good” ammeter has a very small resistance compared to R, which allows current to
easily pass through the ammeter and be measured. When this is the case and the resistor and the
ammeter are in series, so the current measured in the ammeter is essentially determined by R. The
equivalent resistance of R and the ammeter is close to resistance of R because if Rammeter «R then
R + Rammeter R. This is only approximately true for the ammeter you will use in the lab. Because of this,
the most significant source of error in this lab will come from the current measurements. Note that the
voltmeter should not be connected across the (ammeter + resistor) together because the ammeter has a
non-negligible resistance.
Procedure
Before you start: Have your instructor measure the resistances of the resistors, which are next to each
other on the board with the resistive elements shown below. You can also read the values of the resistor
from their colored bands. (The instructions for doing this can be found here
[http://en.wikipedia.org/wiki/Electronic_color_code]). Record the two resistances on your work sheet. These
are your reference values and will be compared with your measured values. You can neglect the errors in
the reference values as they will be much smaller than the errors in your measurements.
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Figure 3 is just above here
Part I-Ohmic Components
Our first measurement will be made on an ohmic component, the resistor
R2 .
1. Make sure the power supply is switched off. Turn the black knob “Current ADJ.” all the way clockwise,
and both the coarse and fine “Voltage ADJ.” knobs all the way counterclockwise to zero. Connect the
power supply, ammeter, and voltmeter to the resistor (see Fig. 3) on your circuit board. Make sure you
wire the setup exactly as shown in Fig 2. You can do this by visualizing and making two “loops” in your
circuit. For the first loop, wire a circuit with the ammeter and the resistor in series: from the + terminal of
the power supply to the red (high voltage) terminal of the ammeter; from the black (low voltage) terminal
of the ammeter to the resistor; from the other end of the resistor (now its low voltage side) to the terminal of the power supply. The next “loop” will involve connecting the voltmeter in parallel to the
resistor. Wire the voltmeter from the high voltage terminal (red) of the voltmeter to the high voltage side
of the resistor and from the low voltage terminal (black) of the voltmeter to the low voltage side of the
resistor. The voltmeter should only be connected across the resistor if your set up is correct. Have your lab
instructor “OK” your setup.
2. Switch the scales on your voltmeter to 20V and your ammeter to 0.2 A. You are going to investigate
how voltage across R2 changes with current through R2 . Increase the voltage, V, in 6 steps from ~ 5 to ~
10 volts. For each voltage step, record the current, I (which is displayed in mA, but should be recorded in
A), flowing through the resistor. Note that the left most knob (“course adjustment”) on the power supply is
used to make large variations in the voltage V, and the middle knob (“fine adjustment”) is used for small
adjustments. Neglect the error in V. For the error in I you can estimate the error as +/- 0.001 A because
this is the last digit in the measurement displayed on the ammeter readout. Enter your measurements into
the table on your worksheet.
3. You now need to plot your data using the plotting tool below. If we plot voltage vs current the slope of
the graph should give us the value of the resistance. Make the plot and record your value for the
resistance (with error) on your worksheet.
x axis label (include units):
y axis label (include units):
Check this box if the fit should go through (0,0). g
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(Don't include (0,0) in your list of points below, it will mess up the fit.)
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6
What kind of errors are you entering below? None
x1:
+/-
y1:
+/-
x2:
+/-
y2:
+/-
x3:
+/-
y3:
+/-
x4:
+/-
y4:
+/-
x5:
+/-
y5:
+/-
x6:
+/-
y6:
+/-
x7:
+/-
y7:
+/-
x8:
+/-
y8:
+/-
x9:
+/-
y9:
+/-
submit
Part II-Resistors in Series
In this part, we will connect and investigate two resistors in series. The equation for the total resistance of
two resistors R1 and R2 in series is
Rs = R1 + R2 (3.2)
Use this equation to calculate the total resistance you should obtain when you connect your two resistors
in series and write this value on your worksheet.
Wire the two resistors,
R1
and
R2 , in series so that you obtain the following circuit.
Figure 4 is just above here
To do this, take the first circuit “loop” from Part I and add R1 in series with R2 . Take the end of R2 that
was previously connected to the negative terminal of the power supply and connect it to one side of R1 .
Then take the free end of R1 and connect that end back to the power supply. Next, remake the second
“loop” by connecting the voltmeter parallel to both R2 and R1 . Wire the high voltage terminal (red) of the
voltmeter to the high voltage side of R2 and the low voltage terminal (black) to the low voltage side of R1 .
Ask your instructor to check your wiring.
Once the resistors are wired correctly measure V and I with the voltage set to ~ 10 V. Calculate the
measured resistance of the series combination using Ohm’s Law. Enter these values on your worksheet.
Calculate the error Rs of Rs from the error in I, neglecting the error in V. Since Rs = V I the relative
error of R is equal to the relative error in I (see expression (E.8) of Uncertainty, Error and Graphs).
Does the calculated value of the equivalent series resistance agree (within error) with the measured value?
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Part III-Resistors in Parallel
In this part, we have two resistors in parallel. The equation for the total resistance of resistors in parallel is
1
Rp
= R1 + R1
1
2
(3.3)
Using this equation and the reference values for the resistors, calculate the expected value for the
equivalent resistance Rp of the parallel resistors and enter it on your worksheet.
Wire the two resistors,
R1
and
R2 , in parallel.
Figure 5 is just above here
This will be slightly different than the last part and will consist of three “loops”. First, make the same first
“loop” as in Part I. The second “loop” will be made by placing R1 in parallel with R2 , which is in the first
“loop”. To do this, connect one end of R1 to the high voltage end of R2 and the other end of R1 to the low
voltage end of R2 . Next you will make a third “loop” by putting the voltmeter in parallel with both R1 and
R2 . To do this connect the high voltage (red) terminal to the high voltage connection to which both R1 and
R2 are wired. Do the same for the low voltage (black) terminal of the voltmeter and the low voltage
connection to both resistors. Ask your instructor to check it.
Once the resistors are wired correctly, measure V and I at a voltage of ~ 10 V. Calculate the measured
resistance of the parallel combination from Ohm’s Law and its error. Remember that as we neglect the
error in the voltage the relative error in R will be the same as the relative error in I. Enter your values on
your worksheet. Calculate the error Rp of the parallel resistance from the error in I neglecting the error
of V as you did in Part II.
Does the calculated value of the equivalent parallel resistance agree (within error) with the measured
value?
Part IV-Non-ohmic Components
Repeat the procedure of Part I using the light bulb instead of the resistor. (You need to rewire the circuit
so that it is like Fig 2 but with the light bulb in the place of R2 . Again, you will be looking at the
relationship between V and I. You should see the bulb light up if you put a few volts across. If not tighten
the bulb. Take ~ 10 data points by varying V from ~1 to ~10V in reasonably uniform steps. Record each
voltage and the associated current. Enter the measurements into the table on your worksheet. You do not
need to record any errors for these data.
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You should now enter the data in to the table below. When you click submit two plots will be produced, the
first one is of voltage vs. current as we did for the ohmic resistor. You should see that this time the plot is
not linear.
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Voltage and Current Values
V I1
V1
A
V2
V
I2
A
V3
V
I3
A
V4
V
I4
A
V5
V
I5
A
V6
V
I6
A
V7
V
I7
A
V8
V
I8
A
V9
V
I9
A
V10
V
I10
A
submit
We can estimate the resistance at each point on the graph by making a linear approximation around each
point. This means we take the change in voltage from the points on either side of the point and divide by
the change in current from the points on either side of the point. For example if I want to find the
resistance at point n, I can approximate it as
Rn =
Vn+1 −Vn−1
In+1 −In−1
(3.4)
The computer will do this for you and make a plot of R vs. V.
Does the bulb behave as an ohmic resistor? Does the bulb resistance increase or decrease with
temperature? Discuss with your partner and with the TA!
lab_3.txt · Last modified: 2011/08/24 13:16 by pmkoch
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