EE 100 – Electrical Engineering Concepts I
Lab 2
Revision 9/01
Name:
___________________________
Partner: ___________________________
Date:
___________
TA:
___________________________
Current Divider
Ammeter
Voltage Divider
Homemade Voltmeter
Wheatstone Bridge
EE 100
Lab Grade:
Lab 2
Grading Sheet
_________ (90 maximum)
Presentation Grade:
_________ (10 maximum)
(organization, clarity, neatness)
Total:
_________ (100 maximum)
Grader’s Comments:
Hand in all lab and work sheets, either stapled securely or in a
folder.
Lab 2
EE 100
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Laboratory Exercise
1.1 Purpose
In this exercise, you will apply the introductory circuit principles to:
1) Vary the range of a provided analog ammeter to measure larger currents.
2) Determine the internal resistance of a battery.
3) Design a “homemade voltmeter” which you will validate against a DMM.
4) Determine an unknown resistance using a Wheatstone Bridge.
1.2
Related Reading
Textbook:
Ch. 2
1.3
Equipment
1) Knight Electronics Mini-Lab
2) Digital multimeter
3) Jumper wires
4) Resistors: 10 kΩ (Qty. 2), 4.7 kΩ, 3 kΩ, 200 Ω, 9.1 Ω and an unknown resistor
1.4 Introduction
The techniques for measuring current, voltage and resistance that were practiced in Lab 1 will
be applied in this lab to further hone your circuit analysis skills. Refer to Lab 1 as needed.
1.5
1.5.1
Experimental Data and Results
Current Divider and Ammeters
1.5.1.1 BackgroundAn analog ammeter, like the 0 to 1 mA meter provided on your Knight board, can be rescaled
to cover a larger current range by utilizing current division. The basic components of the meter
are pictured in Fig. 2-1.
Fig 2-1
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DC current applied to the meter flows through the coil which is positioned in a permanent
magnetic field. This produces a torque on the coil-needle assembly which is proportional to the
applied current. The spring is selected to provide a torque that opposes the applied torque and
gives a full-scale needle deflection when 1 mA is applied.
1.5.1.2 DesignA reasonably accurate model of the meter is shown in the Fig 2-2, where we assume that the
meter box A is an ideal ammeter with 0 series resistance.
Fig 2-2
Measure the Rm of the ammeter provided with your kit using the DMM set to the 200 Ω scale.
Remember to connect the DMM red lead to V/Ω, and don’t forget the meter offset resistance!
Rm = _________
We’ll assume that the meter is fairly accurate and the needle deflects to 1.0 mA, when 1.0 mA
actually passes through it.
Now, make the meter a 10 mA full scale ammeter by placing a shunt resistor across it, as
shown in Fig 2-3.
Fig. 2-3
That is, calculate what Rs needs to be so that 90% of the applied current flows through Rs and
10% flows through Rm. That way, when the meter deflects to 1 mA, 9 mA will be flowing
through Rs, and the total current will always be 10X the meter reading.
Rs = ____________
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Set up your new 10 mA meter. A resistor is provided which should be close in value to the
calculated Rs. Measure and record the actual resistance of Rs, and don’t forget your DMM
offset, since the shunt resistor has a pretty low value.
RsActual = ____________
Now, test your meter with the circuit in Fig. 2-4. The exact resistance of the 1k pot is not
critical, so connect to the two end terminals to get approximately 1 kΩ.
Fig. 2-4
Set POS DC OUT to 0 and power up the Knight board. If the meter needle jumps, turn off the
power and recheck your circuit!
Increase DC OUT as necessary to get the necessary readings to fill in the chart below:
DMM
0.00 mA
Ammeter
% Difference
2.00 mA
4.00 mA
6.00 mA
8.00 mA
10.00 mA
Comment on the sources of error in your ammeter.
If you had used a resistor with the exact calculated shunt resistance, instead of the resistance
used, would your meter readings have been higher or lower? Briefly explain.
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1.5.2
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Voltage Divider
Measure the actual resistance of your 3 kΩ and 10 kΩ resistors, and setup the Fig. 2-5 circuit:
R3k = __________
R10k = __________
Fig. 2-5
Using the DMM, measure:
VAC = _______________
VBC = _______________
Calculate VBC, given VAC. Show your work!
VBC(calc) = _____________
This value should be pretty close to your measured value since the DMM’s internal resistance
is 10 MΩ, which is quite large compared to 3 kΩ!
NOTE: Do not disassemble this circuit any more than necessary. We will use it again in the
next section.
1.5.3
Homemade Voltmeter (HVM)
We will now use the analog ammeter and the 100k Ω potentiometer to make a 0 to 10 volt
voltmeter. We’ll make the ammeter into a voltmeter using the circuit in Fig 2-6.
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Lab 2
Fig. 2-6
We need to determine the resistance setting for the 100k pot, such that when V = 10 volts, the
ammeter will have a full-scale deflection, i.e. 1 mA flowing through it.
Since Rm is negligible, the calculation is just RPOT = V / i ,where V = 10 volts and i = 1 mA.
So, R100k POT = 10 kΩ.
Build the HVM in Fig. 2-6.
Then, to fine tune the HVM, add the DMM as shown in Fig 2-7.
Fig. 2-7
Use the 20 VDC scale on the DMM.
Set V = 5.0 volts using the DMM.
Fine tune the 100k Pot so that the HVM reads “5 volts” (displayed as 0.5 mA; remember, the
HVM reads volts/10, not mA now).
Try V = 2V and V = 10V. The HVM should be within a 2% error. Is it?
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Note: it is not always possible to neglect the internal resistance of a voltmeter. In our case, the
DMM has an internal resistance of about 10 MΩ, while our HVM has an internal resistance of
only 10 kΩ. Our circuit board power supply has an internal resistance of about 500 Ω , so our
readings should be fairly consistent. If the power supply resistance were higher, significant
differences would start to show up.
Recheck the voltage divider from Fig. 2-5. Measure VBC with the DMM and the HVM again
and note the differences. Fill in the table below:
Measured
Calculated
% Error
VBC (DMM)
VBC (HVM)
Note that even with the fairly high internal meter resistance of our HVM, significant loading of
the circuit can occur when a meter is attached to it.
Comments:
You may disassemble your HVM and the voltage divider from before.
1.5.4
Battery Internal Resistance
A battery has a small internal resistance associated with it, such that the battery may be
considered as an ideal voltage source with a resistor in series with it.
Measure the voltage across the AA battery with nothing connected. Since our DMM has such a
high internal resistance, very little current flows during this measurement, so there is little
voltage drop due to the internal resistance. Therefore, the measured voltage may be considered
to be the voltage of the source, Vb as pictured in Fig. 2-8.
Vb = __________
Now measure the resistance of your nominal 9.1 Ω resistor and connect it to the battery as
shown in Fig. 2-8.
A
B
Fig. 2-8
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Lab 2
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Knowing Vb and measuring VAB use the voltage divider equation to calculate Rb. Show your
work.
Rb = ___________
1.5.5
Wheatstone Bridge
The Wheatstone Bridge is the basis for many measurements because it is very sensitive to small
changes in resistance.
Consider the circuit in Fig. 2-9. When the meter (either a voltmeter or an ammeter) reads zero,
the bridge is “balanced,” that is, VBC = 0.
Fig. 2-9
After class, derive the following law for balancing the bridge:
R1
R
= 2
R3 R X
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The DMM is a very sensitive ammeter or voltmeter. On the 20 DCA scale, it can measure
down to .01 µA.
Set up the circuit of Figure 2-10. Use a nominal 10 kΩ resistor for Rx and ask your lab
instructor for a decade resistor box when your circuits ready to go. Measure R1 and R2 as
accurately as possible with the DMM and record below.
Fig. 2-10
Set the DMM to 2m DCA to begin.
The approach will be to set all the resistor settings on the decade box to zero, then begin with
the 10K dial and increase resistance until you see a sign change on the DMM. Return to the
resistance setting prior to the sign change.
Go to the next lower resistance dial and repeat. You must rescale your DMM as you use the
lower resistance dials.
Tune in R3 until the DMM reads 0.00 µA.
Record R3 indicated on the decade box with 5 digit accuracy. Measure Rx with the DMM.
R1 = ________________
R3 =
________________
R2 = ________________
Rx =
________________ (DMM)
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Calculate Rx using the bridge equation:
Rx =
____________ (bridge equation)
Fill in the following table
Rx
Measured with
Wheatstone Bridge
Measured with DMM
How much does Rx vary between the DMM and Wheatstone methods?
% difference = ___________________
Comment on these results.