1. BASIC DC METER
DESIGN
TYLER MAISONNEUVE
FEBRUARY 3RD
, 2015,
TUESDAY AT 8:30 AM
ECE 2100 Circuit Analysis Laboratory

2. Summary
The purpose of this lab was to become familiar with meter movement and shunt
resistance. The importance is designing a circuit using the meter movement and shunt resistor,
because the meter movement can only handle 0.2 mA of current and 100mV.
A meter movement can be used to find the current through a circuit element when
placed in series with it. By finding the voltage across the meter movement (16.2 mV) and
current (47 µA) through it when the current is full scale, the resistance can be found using ohms
law 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐 𝑒 𝑎𝑚𝑚𝑒𝑡𝑒𝑟 =
𝑉𝑜𝑙𝑡𝑎𝑔 𝑒 𝑎𝑚 𝑚𝑒𝑡𝑒𝑟
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑎𝑚𝑚 𝑒𝑡𝑒𝑟
(344.68 Ω). The shunt resistor is found to be 14.37 Ω.
The equivalentresistance forthe metermovementandshuntresistorinparallel is13.79 Ω.
For part two, a voltmeter was designed using the previously measured data for the
meter movement. To do this, a meter movement must be placed in series with a very large
resistor. The voltage for the designed voltmeter can be calculated using a current divider. A
current divider is used to find current when circuit elements are connected in parallel. This
voltmeter was designed with a full scale voltage of 10 volts in mind.
Part three of the lab involved calculating the voltage across two resistors when they had
the same resistance. The two resistances were used were 1 k Ω and 100k Ω. Thishad to be done by
measuringthe voltage directly,withamultimeter,andusingthe designedvoltmeter. Full scale current
and voltage usedforthispart was6 mA and 12 voltsrespectively.
Some useful Variables:
𝑅 𝑚 = 𝑀𝑒𝑡𝑒𝑟 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑅 𝑛 = 𝑅𝑒𝑠𝑖𝑎𝑡𝑛𝑐𝑒 𝑖𝑛 𝑠𝑒𝑟𝑖𝑒𝑠 𝑤𝑖𝑡ℎ 𝑚𝑒𝑡𝑒𝑟 𝑓𝑜𝑟 𝑣𝑜𝑙𝑡𝑚𝑒𝑡𝑒𝑟
𝑅 𝑠 = 𝑆ℎ𝑢𝑛𝑡 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑓𝑜𝑟 𝑑𝑒𝑠𝑖𝑔𝑛𝑒𝑑 𝑎𝑚𝑚𝑒𝑡𝑒𝑟
𝐼𝑓𝑠 = 𝐹𝑢𝑙𝑙 𝑠𝑐𝑎𝑙𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑡
𝐼 𝑚 = 𝑀𝑒𝑡𝑒𝑟 𝑐𝑢𝑟𝑟𝑒𝑛𝑡
𝑉𝑓𝑠 = 𝐹𝑢𝑙𝑙 𝑠𝑐𝑎𝑙𝑒 𝑣𝑜𝑙𝑡𝑎𝑔𝑒
𝑉𝑚 = 𝑉𝑜𝑙𝑎𝑡𝑔𝑒 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑤𝑖𝑡ℎ 𝑚𝑒𝑡𝑒𝑟 𝑑𝑒𝑠𝑖𝑔𝑛𝑒𝑑 𝑣𝑜𝑙𝑡𝑚𝑒𝑡𝑒𝑟 𝑟𝑒𝑎𝑑𝑖𝑛𝑔
𝑉 = 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑓𝑜𝑢𝑛𝑑 𝑖𝑛 𝑝𝑎𝑟𝑡 𝑡ℎ𝑟𝑒𝑒

3. Results of the Laboratory Experiment
Part One:
To design an ammeter to measure the current through a circuit, a few things have to be found.
The firstisthe internal resistance of the metermovementitself.Thiswasfoundtobe 344.68 Ω. Once the
resistance of the meter is known, the formula 𝑅 𝑠 =
𝐼 𝑚∗𝑅 𝑚
𝐼 𝑓𝑠−𝐼 𝑚
can be used to find the shunt resistance
needed for the meter movement. To find the current through the circuit with the 1k Ω resistor, use the
formula 𝐼 =
𝑅 𝑚
𝑅 𝑒𝑞
∗ 𝐼 𝑚. The 𝐼 𝑚 value is the reading on the meter movement which is measured in micro
Amps. These are the values recorded in the table (Figure 1.1) below. To calculate percent error:
⃒𝑑𝑒𝑠𝑖𝑔𝑛𝑒𝑑 − 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑⃒
𝑑𝑒𝑠𝑖𝑔𝑛𝑒𝑑
∗ 100 = % 𝑒𝑟𝑟𝑜𝑟
Figure 1.1
Figure 1.2
The plot to the right represents the calibration
Curve for the data obtained with the ammeter
Vs. the data obtained using the multimeter.
Meter Reading
(Micro Amps)
Vin
(volts)
Designed ammeter current
(mA)
standard ammeter current
(mA) Error (%)
20 0.5 0.4997 0.560 0.12
35 1.0 0.9244 1.000 8.00
50 1.5 1.399 1.450 3.60
77 2.0 1.924 1.960 1.80
95 2.5 2.370 2.390 0.84
118 3.0 2.948 2.980 1.10
140 3.5 3.498 3.530 0.91
157 4.0 3.922 3.950 0.71
176 4.5 4.398 4.430 0.73
200 5.0 4.997 4.980 0.34
Average % error = 1.815%

4. 0
2
4
6
8
10
12
0 5 10 15
Design(Volts)
DMM (Volts)
Design vs. DMM
Voltage
Part two:
Below are the results from the designed voltmeter. To find the voltage of a specific element,
the designed voltmeter must be connected in parallel with it. The formula
𝑉 𝑓𝑠
𝐼 𝑓𝑠
− 𝑅 𝑚 = 𝑅 𝑠 gives
the value of resistance that must be in series with the meter movement with a full scale current
of 0.2 mA. This resistance is 49,655Ω. Using the reading from the meter movement, the values
were calculated and recorded in the following table (Figure 2.1) using the formula
𝑉𝑚 = (𝑅 𝑛 + 𝑅 𝑚 ) ∗ 𝐼 𝑚 . Also, the calibration plot (Figure 2.2) is pulled directly from the table,
also shown below.
Figure 2.1 Figure 2.2
Meter
Reading
(micro Amps )
Vin
(Volts)
Designed
Meter
(Volts)
DMM
(Volts)
%
Error
15 1 0.75 1.01 35.00
36 2 1.80 1.96 8.90
57 3 2.85 3.01 5.40
77 4 3.85 3.98 3.40
99 5 4.95 5.06 2.20
118 6 5.90 6.02 2.00
137 7 6.85 6.95 1.50
157 8 7.85 8.00 1.90
178 9 8.90 8.90 0.00
200 10 10.00 9.97 0.30
Average % error = 6.06 %

5. Part three:
The final part of this lab involved measuring the voltage across a resistor when another resistor
of equal resistance was placed in series with it. This can be done using the voltage divider
𝑉 =
𝑅2
𝑅1 +𝑅2
∗ 𝑉𝑖𝑛. To find the voltage using the designed voltmeter, the formula
𝑉𝑓𝑠 = 𝐼𝑓𝑠( 𝑅 𝑛 + 𝑅 𝑚) is used. Lastly, to find the voltage using the DMM, simply place the leads
on the terminals of the resistor. These results were recorded in the table below, Figure 3.1, and
done using a 1 k Ω resistorand a 100 k Ω resistor.
Figure 3.1
Resistor
(k Ω)
Calculated
Voltage
(Volts)
DMM
Voltage
(volts)
Design
Voltmeter
Voltage
(Volts)
R1=R2=1 6.00 5.99 5.97
R1=R2=100 6.00 5.98 3.00

6. Conclusion to the results
The ideal resistance of an ammeter is 0, which is impossible in the real world. Through this
experiment, however, the designed ammeters shunt resistance was significantly lower than the
resistance of the in series resistor. Since the shunt resistor takes most of the current in the
designed ammeter, its value is used when computing the equivalent resistance. Because of
this, the theoretical values and experimental values were very close. For the designed
ammeter, there was an average error of 1.815%. This could have been caused by multiple
errors such as the resistance of the resistors not being perfect. Resistors used for this
experiment have a tolerance of 5%. Other errors could be from reading the designed ammeter.
Values for where the needle lies had to be approximated to the nearest 10th because that was
the accuracy of the device. Lastly, errors could have come from the power source. They only
show output to the tenth, which could slightly skew data.
For the second part of the lab, a voltmeter was designed. This was again done with the meter
movement. The ideal resistance of a voltmeter should be infinite because it is connected in
parallel with the circuit element. When the resistance of a voltmeter is infinite, there is no
current flowing through it, thus no voltage across the terminals. A 49,655k Ω resistorconnected
inserieswiththe metermovementdidprove toserve asan accurate voltmeter,asthe average percent
error was6.06%. This,however,islargerthanthe errorof the ammeter.Thisispartlydue to the fact
that the closerthe inputvoltage getstothe Full scale voltage,the more accurate the device is.Alsothe
resistance wasnotinfinite,thereforenotanideal voltmeter.
Part three of the lab ran into trouble astime wasrunningout.To allow studentstofinishthe lab
successfullyandwalkawaywiththe knowledgetofinish,the TA explainedthe formulastofindthe
voltage theoreticallyandbymeansof the designedvoltmeter.There wasverylittle errorinthe values
calculatedtheoreticallyanddone usingthe voltmeterdesign.Thishastodo withthe fact that there
were nolaboratoryimperfectionstogetinthe way.All inall,there isno doubtthat there are waysto
improve thismethodof measuring the currentandvoltage throughandacrosscircuitelements
respectively.