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# Curriculum and Labs for Engineering Education

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## myDAQ mini-lab: Equivalent Resistance III – Series-Parallel

Course Linkage: Linear Circuit Analysis >> Resistive Circuits >> Series and Parallel Resistors

Measurement Techniques: ELVISmx DMM (ohmmeter)

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### Introduction

Overview: Two previous myDAQ mini-labs (Equivalent Resistance I – Seriesand Equivalent Resistance II – Parallel) explored resistor circuits that were either entirely series or entirely parallel. Practical circuits generally contain both series and parallel combinations. Reducing these circuits to a single equivalent resistance is an important analysis skill.

Objectives: In this mini-lab you will:

• Learn about resistor color codes
• Measure the resistance of individual resistors
• Compare measured resistance to nominal value
• Predict the equivalent resistance of mixed series-parallel-connected resistors
• Compare measured equivalent resistance to expected values

### Equipment

• NI myDAQ
• Connecting wire
• Resistors, ¼-W 5% carbon film: 10K (two), 33K (two), 47K (two)

### Deliverables

• Submit your work in the form of a homework set problem or lab notebook entry according to the requirements of your instructor
• Submit your work for each underlined boldface item, and clearly label the item with its section letter and task number

### A. Experience series-parallel resistors by measurement:

NOTE: Proceed directly to Step 10 if you have already completed the myDAQ mini-lab Equivalent Resistance I – Seriesand your breadboard still contains the same resistors that you measured earlier; you will need those measurements for this mini-lab.

1. Study the short article Resistor Color Codesto learn how to read the nominal value encoded in the color bands that encircle a resistor. For example, the 10K resistor has the color code “orange-orange-orange” = 33 x 103 = 33 kW.
2. Record the color bands for the 10K and 47K resistors.
3. Place the six resistors on your breadboard as shown in Figure 1. Use the same hole spacing to match the wiring that will be added later.
4. Start the ELVISmx Instrument Launcher and click “DMM.” Choose the ohmmeter instrument (the “ohm” symbol, capital omega), select autoranging (choose “Auto” for “Mode”) and click the green “Run” button:

5. Connect the DMM probes to the ohmmeter side (red volt-ohm and black COM jacks) as shown on the ELVISmx DMM “Banana Jack Connections” graphic.
6. Touch the DMM probe tips together to ensure that the ohmmeter properly reads zero or at most a fraction of an ohm. The probe cables have negligible resistance compared to the resistors used in this mini-lab.
7. Measure and record the resistance of each of the resistors R1 through R6.
8. Create a data table with four columns: resistor label, nominal value (i.e., the value indicated by the color code), measured value, and percentage difference from nominal. Calculate the last column as ((RmeasuredRnominal)/Rnominal) x 100%.
9. Report the largest percentage difference and whether or not it falls within 5% of the nominal value; this is the significance of the gold 5% tolerance band on the resistor.
10. Connect the resistors as shown in Figure 2 (click the image to see higher resolution):
11. Measure and record the resistance between terminals A and B.
12. Rewire your breadboard to connect the resistors as shown in Figure 3:
13. Measure and record the resistance between terminals C and D.

### B. Learn the underlying principles:

The following video tutorial describes how to calculate the equivalent resistance of the two circuits you measured in the previous section:

### C. Connect the principles to your measurements:

1. Rewire your breadboard to match the circuit shown in Figure 4:
3. Calculate the equivalent resistance between the following terminal pairs using your measured resistance values for R1 through R6: A-B, B-C, C-D, and A-D.
4. Measure and record the resistance between the same terminal pairs: A-B, B-C, C-D, and A-D.
5. Calculate the percentage difference between your measured value and your calculated value.
6. Report the maximum percentage difference between your calculated and measured values. If the difference is more than 1%, review your wiring and calculations and make corrections as necessary.

1. Respond: In which of the four terminal pairs from the previous section does the resistor R1 actually not contribute to the effective resistance? Explain why.
2. Draw a circuit based on the six resistors R1 through R6 (use the same layout as Figure 1) that has an equivalent resistance of 45 kW. Hint: The parallel combination of two equal-valued resistors has half the resistance.