lab 3 report final

Electric Circuits ENGR 2790U

Laboratory 3 Voltage and current dividers, Wheatstone

bridge and basic 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 understand 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 the 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. The Agilent power supply was used to supply a current of 5 mA

3. The voltage limit was set to 12V for safety purposes

4. The output currents across the circuit were measured and recorded in Table 3-8

5. 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 and 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 3-

10

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 over 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 10k 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 (k) 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

% Error in output voltage 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%

Sample error calculation = |

| |

|

The same error calculation format was used throughout the laboratory.

Sample calculated output voltage =

Sample calculated voltage gain = =

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 an 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 2k, 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 (k) 1 2 3.3 4.7 5.6 10



% Error in output voltage 0% 0% 0% 0% 0% 0%



% Error in voltage gain 0% 0% 0% 0% 0% 0%

Sample calculated output voltage:

Sample calculated voltage gain:

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 4.7k. 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 (k) 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

% Error in output current 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%

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 and 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

Open Circuit

Calculated

Short Circuit

Simulated

Open Circuit

Simulated

Short Circuit

IV1 (mA) 9.75 10.106 9.75 10.106

IR1 (mA) 6 5.053 6 5.053

IR2 (mA) 6 6.947 6 6.947

IR3 (mA) 3.75 5.053 3.75 5.053

IR4 (mA) 3.75 3.158 3.75 3.158

IAB (mA) 1.895 0 1.895 0

VR1 (V) 6 5.053 6 5.053

VR2 (V) 6 6.947 6 6.947

VR3 (V) 3.75 5.053 3.75 5.053

VR4 (V) 8.25 6.947 8.25 6.947

VAB (V) 2.25 0 2.25 0

Lab Tasks:

3.4.1 Voltage Divider:

The circuit in Figure 3.1 was constructed. R1 was set to 10k 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 (k) 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

% Error 0.497% 0.452% 36.650% 0.266% 0.237% 0.253%

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 (k) 1 2 3.3 4.7 5.6 10



% Error 1.02% 0.69% 9.94% 0.78% 0.81% 0.88%



% Error 1.02% 0% 9.94% 0.78% 0.81% 0.88%

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 10M resistors had measured value of:

R1=9.8809 M R2=9.8312 M

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

Measured Value

% Error Remarks

R1 (M) 10 9.8809 1.19% Within Tolerance

R2 (M) 10 9.8312 1.69% Within Tolerance

VR1 (V) 4.998 3.324 33.49 % High

VR2 (V) 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. The 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 very

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 4.7k, 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 k 2k 3.3k 4.7k 5.6k 10k

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


V1+ 11.556 12 3.7%

VA 8.220 8.25 0.36%

VB 5.940 6 1.00%

IAB 1.624 1.895 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 10M were used in the voltage divider, not much changed. The voltage was

relatively equal across each resistor, but the percent error 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 very 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 out of six of the measured

outputs would be within the tolerance. One of 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 k 2k 3.3k 4.7k 5.6k 10k

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.

Resistor

Measured

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



V1+ 11.556 12 3.7%

VA 8.220 8.25 0.36%

VB 5.940 6 1.00%



V1+ 11.556 12 3.7%

VA 8.220 8.25 0.36%

VB 5.940 6 1.00%

IAB 1.624 1.895 14.40%%

Table 3-9 and 3-10 respectively re-calculated and re-simulated using actual measured

resistances



V1+ 11.956 12 0.37%

VA 8.247 8.25 0.036%

VB 5.963 6 0.62%



V1+ 11.956 12 0.37%

VA 8.220 8.25 0.036%

VB 5.963 6 0.62%

IAB 1.624 1.895 14.40%%

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 Ohms 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:

R3I1 +R5I1 -R5I3 +R1I1 -R1I2=0

(R3+R5+R1)I1 -R1I2 -R5I3=0

2.9946I1 -0.9979I1 -0.9974I3=0

Branch 2:

12 +R1I2 -R1I1 +R2I2 -R2I3 = 0

-R1I1 + (R1+R2)I2 -R2(I3) = -12

-0.9979I1+ 1.9875I3 -0.9896I3 = - 12

Branch 3:

R5I3 -R5I1+ R4I3+ R2I3- R2I2=0

-R5I1 -R2I2+ (R5+R4+R2)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 component of the lab, however from the

assistance of the lab TA, the questions were answered. Overall, the lab experiment was

accomplished successfully.

lab 3 report final

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