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A lab manual for ee 100 - electrical engineering concepts i, lab 2. Students will learn how to apply circuit principles to measure larger currents, determine battery internal resistance, design a homemade voltmeter, and use a wheatstone bridge. The lab includes instructions, related reading, equipment list, and experimental data.
Typology: Lab Reports
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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 Design-
A 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-
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-
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 = ____________
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.
Rs (^) Actual = ____________
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-
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 Ammeter % Difference 0.00 mA
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.
Fig. 2-
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 R (^) POT = 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-
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. Comment on the error of the HVM at the different voltages.
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.
Fig. 2-
A B
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-
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.
R2 = ________________ Rx = ________________ (DMM)
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.
