Electric Circuits ENGR 2790U Laboratory 3 – 3 – Voltage Voltage and current dividers, Wheatstone bridge and basic circuit circuit analysis October 16, 2014 Raj Panchal - 100520916 Kevin Cordy - 100488529
Objective: There were many objectives to complete throughout the duration of the laboratory. The first was to gain hands on experience with voltage/current supplies, ammeters, voltmeter functions, and variable resistors. Another objective was to study current and voltage dividers, as well understanding and validating the function of a Wheatstone bridge. The last objective was to experience the internal resistance of a multimeter and un derstand the effect on the results.
Components and Instruments: The components and instruments used in the laboratory were as follows in Table 1: Table 1 – Components and Instruments Utilized
Procedure: 3.4.1 Voltage divider
1. Circuit as shown in Figure 3-1 was set up on the breadboard using +25V power supply from Agilent power supply
2. A resistance of 10 kOhm was constantly used for R1 while for R2 1, 2, 3.3, 4.7, 5.6 and 10 kOhm resistors were used 3. The output voltages were recorded on table 3-5 along with the calculated values from pre-lab calculations 4. Another resistor RL was added to the same circuit in parallel with R2 5. V1 was used with a value of 10V, R1 and R2 had values of 2 kOhm while for RL 1, 2, 3.3, 4.7, 5.6 and 10 kOhm resistors were used 6. Voltage values for each were measured
7. Voltage values were recorded on table 3-6 along with calculated values for the voltage from pre-lab calculations 8. Two resistors, R1 and R2 with values of 10 MOhm each were obtained, and measured using DMM 9. The circuit from figure 3-1 was built again on th e breadboard with a power supply of 10V 10. Voltages were measured across R1 and R2, and were recorded on table 3-7 11. Remarks were made on the accuracy of nominal value vs. measured value and were analysed by the %Error 3.4.2 Current divider
1. The circuit from figure 3-2 was constructed on the breadboard where resistor R1 had a value of 4.7 kOhm and R2 had values of 1, 2, 3.3, 4.7, 5.6 and 10 kOhm
2. 3. 4. 5.
The Agilent power supply was used to suppl y a current of 5 mA The voltage limit was set to 12V for safety purposes The output currents across the circuit were measured and recorded in Table 3-8 Calculations from pre-lab were also recorded in table 3 -8, these values were analysed using %Error
3.4.3 Wheatstone bridge 1. The circuit in figure 3-3 was constructed on the breadboard using resistors of values 1, 2, and 3.3 kOhm for R1, R3, and R4 respectively with a supply voltage of 10V 2. Variable 1 kOhm resistor was used for R2 3. The values for R1, R3, and R4 were measured using DMM 4. The power source was attached to the circuit and R2 was adjusted to get 0 current between A and B 5. The circuit was depowered and the resistance of R2 was recorded
6. R3 was replaced with a 4.7k resistor and steps 3-5 were repeated 7. Steps 1 – 4 were repeated with different values for R3
3.4.4 Basic Circuit Analysis Techniques
1. The circuit from figure 3-3 was built, the resistor values were measured an d recorded
2. The voltages at each node were measured using the DMM 3. The values were recorded onto table 3-9 along with the calculations from pre-lab tasks, these values were then analysed using %Error 4. The open circuit between A and B was replaced with DMM to measure the short circuit current, this was repeated with the other voltages from previous table (Table 3-9) 5. A 1kOhm resistor was added in series with the ammeter in the central branch and the voltage and current measurements were repeated, the values were recorded onto table 310 6. The values from the open and short circuit tests were compared to pre-lab task values 7. The lab experiment was concluded
Results: Prelab Tasks:
The prelab tasks for the third laboratory were designed to ensure the objectives and topics of the experiment were well understood. These tasks involved a review of current division, voltage division, loaded resistors, as well as going ov er the function of a Wheatstone bridge. The first section of the prelab tasks covered voltage division. The tasks associated with voltage division were based off of Figure 3.1, which follows:
The gain and output voltage of the voltage divider with a fixed R1 value of 10kΩ was calculated and placed into Table 3.1. The voltage source was set at 10V. Simulated values were obtained from a simulated circuit in Multisim. Table 3.1: Calculated and Measured Values in a Voltage Divider Circuit R2 Values (kΩ)
1
2
3.3
4.7
5.6
10
Calculated output voltage (V)
0.909
1.667
2.481
3.20
3.59
5.0
Simulated output voltage (V)
0.909
1.667
2.481
3.197
3.59
5.0
0%
0%
0%
0.09%
0%
0%
Calculated voltage gain
0.0909
0.1667
0.2481
0.320
0.359
0.5
Simulated voltage gain
0.0909
0.1667
0.2481
0.3197
0.359
0.5
% Error in voltage gain
0%
0%
0%
0.09%
0%
0%
% Error in output voltage
Sample error calculation =
| | | |
The same error calculation format was used throughout the laboratory.
Sample calculated voltage gain = = Sample calculated output voltage =
The percent errors displayed in Table 3.1 show that the calculations were done correctly, as well as the construction of the circuit in Multisim. Possible causes for any error could be resistance due to the simulated wires and/or the internal resistance of the simulated multimeter. If R2 was replaced with an open circuit, there would be 10V across it. If there was a n short circuit, 0V would cross it. The same circuit as in Figure 3.1 was used again, but this time a loaded resistor was added. R1 and R2 were kept constant at 2kΩ, and the voltage source was set to 10V. The output voltage was calculated, as well as the voltage gain. Simulated values were obtained from a simulated circuit in Multisim. Table 3.2 displays these values: Table 3.2: Calculated and Measured Values in a Loaded Voltage Divider Circuit RL Values (kΩ)
1
2
3.3
4.7
5.6
10
Calculated output voltage (V)
2.5
3.333
3.837
4.123
4.242
4.545
Simulated output voltage (V)
2.5
3.333
3.837
4.123
4.242
4.545
% Error in output voltage
0%
0%
0%
0%
0%
0%
Calculated voltage gain
0.25
0.3333
0.3837
0.4123
0.4242
0.4545
Simulated voltage gain
0.25
0.3333
0.3837
0.4123
0.4242
0.4545
% Error in voltage gain
0%
0%
0%
0%
0%
0%
Sample calculated voltage gain: Sample calculated output voltage:
The percent errors were all 0%, indicating the theoretical process directly matches the experimental process. Figure 3.2 is used for the current division section of the prelab. An input current of 50mA was used, and R1 was fixed at 4.7kΩ. The current gain and output current were computed and
placed into Table 3.3, along with the simulated values obtained from Multisim.
Table 3.3: Calculated and Measured Values in a Current Voltage Divider Circuit R2 Values (kΩ)
1
2
3.3
4.7
5.6
10
Calculated output current (mA)
41.228
35.075
29.375
25
22.816
15.986
Simulated output current (mA)
41.223
35.072
29.374
25.011
22.808
15.975
0.01%
0.009%
0%
0.04%
0.04%
0.08%
Calculated current gain
0.8246
0.7015
0.5875
0.5
0.4563
0.3197
Simulated current gain
0.8247
0.7014
0.58748
0.50022
0.45616
0.031946
% Error in current gain
0.01%
0.01%
0.003%
0.04%
0.03%
0.08%
% Error in output current
Sample calculated output current =
Sample calculated current gain =
From Table 3.3, the errors are considerably low. This indicates the experimental method matches the theoretical method very well. The small error may be due to the simulated wire resistance in Multisim, or the internal resistance of the virtual multimeter. The Wheatstone bridge in Figure 3.3 was used as the model for all of the calculation in Table 3.4. The current and voltage across each resistor were calculated an d simulated (using Multisim), and organized into Table 3.4. The calculations and simulations were done assuming an open circuit, as well as a short circuit.
Table 3.4: Wheatstone Bridge Open and Short Circuit Data – Calculated and Simulated Variable Calculated Calculated Simulated Simulated Open Circuit Short Circuit Open Circuit Short Circuit 9.75 10.106 9.75 10.106 IV1 (mA) 6 5.053 6 5.053 IR1 (mA) 6 6.947 6 6.947 IR2 (mA) 3.75 5.053 3.75 5.053 IR3 (mA) 3.75 3.158 3.75 3.158 IR4 (mA) 1.895 0 1.895 0 IAB (mA) 6 5.053 6 5.053 VR1 (V) 6 6.947 6 6.947 VR2 (V) 3.75 5.053 3.75 5.053 VR3 (V) 8.25 6.947 8.25 6.947 VR4 (V) 2.25 0 2.25 0 VAB (V)
Lab Tasks: 3.4.1 Voltage Divider:
The circuit in Figure 3.1 was constructed. R1 was set to 10kΩ and the source voltage was 10V. The output voltages were measured and placed in Table 3.5, along with the calculated value from the prelab. Table 3.5: Calculated and Measured Values in a Voltage Divider R2 Values (kΩ)
1
2
3.3
4.7
5.6
10
Calculated output voltage (V)
0.909
1.667
2.481
3.2
3.59
5
Measured output voltage (V)
0.91354
1.6595
1.8156
3.1915
3.5815
5.0127
0.497%
0.452%
36.650%
0.266%
0.237%
0.253%
% Error
Sample calculations are the same as the ones for Table 3.1. All of the errors are low except one entry, in which the experimental error could have been caused due to a faulty breadboard or incorrect circuit build. But, the other entries with relatively low errors would have had sources of error such as unaccounted resistance in the wires and multimeter. It can be said that the theoretical current division formula applies in the real world very well because the experimental errors were low values. The same circuit as above was used, but this time a loaded resistor was added. The output voltages and voltage gains were simulated, and placed into Table 3.6. Calculated values were form the prelab. Table 3.6: Calculated and Measured Values in a Loaded Voltage Divider RL Values (kΩ)
1
2
3.3
4.7
5.6
10
Calculated output voltage (V)
2.5
3.333
3.857
4.123
4.242
4.545
Simulated output voltage (V)
2.5255
3.356
3.4735
4.1553
4.2762
4.5852
1.02%
0.69%
9.94%
0.78%
0.81%
0.88%
Calculated voltage gain
0.25
0.333
0.3857
0.4123
0.4242
0.4545
Simulated voltage gain
0.25255
0.333
0.34735
0.41553
0.42762
0.45852
1.02%
0%
9.94%
0.78%
0.81%
0.88%
% Error
% Error
Sample calculations are similar to those in Table 3.1. Once again, the error was calculated and turned out to be relatively low. The theory matched the real life circuit well.
The two 10MΩ resistors had measured value of: R1=9.8809 MΩ R2=9.8312 MΩ The circuit in Figure 3.1 was built using the resistors mention above, R1 and R2. The voltage across each resistor was measured and placed into Table 3.7: Table 3.7: Calculated and Simulated Values Comparison in a Voltage Divider Resistor
Nominal Value
R1 (MΩ)
10
Measured Value 9.8809
R2 (MΩ)
10
VR1 (V) VR2 (V)
% Error
Remarks
1.19%
Within Tolerance
9.8312
1.69%
Within Tolerance
4.998
3.324
33.49 %
High
5.003
3.2797
34.45%
High
The voltage measurements had an okay percent error (sub 35%) and the resistors were within the tolerance indicated by their colour bands. T he theoretical values for the voltages across R1 and R2 should include the shunt resistance because the multimeter does not account for it. Thus, it affects the values and should be considered. However, the shunt resistance is usually a ver y small value and can often be negated when dealing with simple problems. 3.4.2 Current Divider:
The circuit in Figure 3.2 was made. R1 had a value of 4.7kΩ, while R2 was variable. The output current was measured, and also the source current. These values were placed into Table 3.8: Table 3.8: Calculated and Simulated Values Comparison in a Current Divider R2 Values
1 kΩ
2kΩ
3.3kΩ
4.7kΩ
5.6kΩ
10kΩ
Measured source (A)
4.7208
4.6889
4.6857
4.68441
4.6407
3.7878
Measured output (A)
3.8844
3.3099
3.1901
2.3377
2.1226
1.2055
Calculated output (A)
3.893
3.289
2.753
2.342
2.118
1.211
% Error
0.22%
0.63%
13.70%
0.18%
0.22%
0.46%
The sample calculations are similar to those from Table 3.3. The % errors are, once again, low, which is expected. The current division formula is accurate and correct when compared to real life circuits.
3.4.3 Wheatstone bridge: Table 3.9: Calculated and Measured Values in open circuit conditions Variable
Measured (V)
Calculated (V)
%Error
V1+
11.556
12
3.7%
VA
8.220
8.25
0.36%
VB
5.940
6
1.00%
Table 3.10: Calculated and Measured Values in short circuit conditions Variable V1+ VA VB IAB
Measured (V)
Calculated (V)
11.556
12
8.220
8.25
5.940 1.624
6
1.895
%Error 3.7% 0.36% 1.00% 14.40%%
Analysis Questions: 1. When the circuit became loaded, the output voltages were higher than when it was unloaded. Thus, there was a higher voltage gain. The practical implication this would have on a voltage divider could be a main power supply: the loaded voltage is variable to how many devices are plugged into the main power. The more devices, the higher the loaded resistance, and the higher the output voltage becomes. 2. When the 10MΩ were used in the voltage divider, not much changed. The voltage was relatively equal across each resistor, but the percent e rror was quite high at around 35%. This means the effect of a large resistance makes the voltage divider formula not as practical. 3. The measurements made with the current divider were ver y close to the calculated values using a current division formula. Table 3.8 displays the values, including the errors: The tolerances on the resistors are all 5%, meaning that five o ut of six of the measured outputs would be within the tolerance. One o f the outputs had an error above the 5% tolerance, meaning a faulty resistor was used, or the breadboard malfunctioned, or the circuit was not built correctly. Table 3.8: Calculated and Simulated Values Comparison in a Current Divider R2 Values
1 kΩ
2kΩ
3.3kΩ
4.7kΩ
5.6kΩ
10kΩ
Measured source (A)
4.7208
4.6889
4.6857
4.68441
4.6407
3.7878
Measured output (A)
3.8844
3.3099
3.1901
2.3377
2.1226
1.2055
Calculated output (A)
3.893
3.289
2.753
2.342
2.118
1.211
% Error
0.22%
0.63%
13.70%
0.18%
0.22%
0.46%
4. The Wheatstone bridge method is an accurate method for determining the voltage and resistance values in a circuit. This can be seen by comparing the measured values from table 3-9 and 3-10 to the calculated values. The percent error is very low which proves that the Wheatstone bridge is an accurate method. 5. For the Basic Circuit Analysis Technique section, the following tables are re-computed and re-simulated results using the measured resistance values in place of those computed and simulated in the pre-lab. Measured Resistor Resistance R1 0.9979k R2 0.9896k R3 0.9993k R4 2.1963k R5 0.9974k
Table 3-9 and 3-10 respectively, obtained from the Lab Table 3.9: Calculated and Measured Values in open circuit conditions Variable
Measured (V)
Calculated (V)
%Error
V1+
11.556
12
3.7%
VA
8.220
8.25
0.36%
VB
5.940
6
1.00%
Table 3.10: Calculated and Measured Values in short circuit conditions Variable V1+ VA VB IAB
Measured (V) 11.556
Calculated (V) 12
8.220
8.25
5.940 1.624
6
1.895
%Error 3.7% 0.36% 1.00% 14.40%%
Table 3-9 and 3-10 respectively re-calculated and re-simulated using actual measured resistances Table 3.9: Calculated and Measured Values in open circuit conditions Variable
Measured (V)
Calculated (V)
%Error
V1+
11.956
12
0.37%
VA
8.247
8.25
0.036%
VB
5.963
6
0.62%
Table 3.10: Calculated and Measured Values in short circuit conditions Variable V1+ VA VB IAB
Measured (V) 11.956
Calculated (V) 12
8.220
8.25
5.963 1.624
6
%Error 0.37% 0.036% 0.62% 14.40%%
1.895 The changes in the resistance for each resistor caused changes in the voltage values as well. However these changes were minimal. As the resistor was slightly lowered, the current was increased due to Ohm’s law, since resistance and current are inversely proportional. 6. 7. a. The calculated value for the current in central branch agrees with the calculated value of the current which is 1.895 mA. The calculation gives 0% error, therefore this is an acceptable value. b.
Branch 1: R 3I1 +R 5I1 -R 5I3 +R 1I1 -R 1I2=0 (R 3+R 5+R 1)I1 -R 1I2 -R 5I3=0 2.9946I1 -0.9979I1 -0.9974I3=0 Branch 2: 12 +R 1I2 -R 1I1 +R 2I2 -R 2I3 = 0 -R 1I1 + (R 1+R 2)I2 -R 2(I3) = -12 -0.9979I1+ 1.9875I3 -0.9896I3 = - 12 Branch 3: R 5I3 -R 5I1+ R 4I3+ R 2I3- R 2I2=0 -R 5I1 -R 2I2+ (R 5+R 4+R 2)I3=0 -0.9974I1 -0.9896I2 +4.19833I3= 0 The results for these I values are 4.96 mA, 9.89 mA, and 3.43 mA for I1, I2, and I3. These values are within the acceptable error range, which is 5% error range.
Conclusion: In this lab experiment multiple objectives were accomplished. These included hands on experience with voltage/current supplies, ammeters, voltmeter functions, and variable resistors; study of current and voltage dividers, as well understanding and validating the function of a Wheatstone bridge; and to experience the internal resistance of a multi meter and understand the effect on the results. In the conclusion of the experiment it was found that voltage divider and Wheatstone bridge, both are accurate methods in application. It was found that voltage and current dividers are used to provide a fraction of the supplied voltage from the source. The Wheatstone circuit experiment was also done successfully utilizing the XK 150 kit. There were a few difficulties faced during the experiment. Measuring the values of all of the resistors was one of the major difficulties due to the minimal time provided to accomplish the lab, this was later solved by making the process faster due to experience. Another difficulty faced during the experiment was understanding the Wheatstone bridge compo nent of the lab, however from the assistance of the lab TA, the questions were answered. Overall, the lab experiment was accomplished successfully.
