List the equipment that you will use for this experiment.

Components:

• R1 - 68 K Ohm Resistor
• R2 - 68 Ohm Resistor
• R3 - 6.8 K Ohm Resistor
• R4 - 68 K Ohm Resistor
• R5 - 680 Ohm Resistor
• R6 - a potentiometer of your choice

• Measure the voltage an ohm meter generates across an unknown resistance.
• Analyze a circuit using Kirchoff's Voltage and Current Law.
• Verify your analysis with voltage and current measurements.
• Create any necessary data tables.
• Create any necessary general equations.
• Verify the Maximum Power Transfer Theorem.
• Use a spreadsheet software to manipulate data.
• Indirectly measure the internal resistance of a power supply.
• Indirectly measure the voltage burden caused by a current meter.

Refer to the specifications concerning the Keithley Model 175 Digital Multimeter (DMM).  Determine the appropriate "Maximum Voltage Across An Unknown" rating if the DMM were to be used to measure the following test resistances on a scale that provides maximum resolution.

Use these test resistances:
1)  680 Ohm
2)  6.8 K Ohm

Verify that both of the Keithley 175s located on the bench meets the specifications you researched earlier.
Put calculated and mesured values for both resistors in Data Table 1.

Caution: You should never attempt to measure the resistance of a resistor while that resistor is in a circuit.

                                                Figure #1

2. - (PreLab) Node Voltage Method - Analysis

Use the node voltage method to analyze the dc circuit shown in Figure #1.  Generate the necessary general equations from the node voltage analysis that will give you:

1. Voltage drop across each resistor.
2. Current through each resistor.
3. Total power consumed by the circuit.

Use the mesh current method to analyze the dc circuit shown in Figure #1.  Generate the necessary general equations from the mesh current method that will give you:

1. Voltage drop across each resistor.
2. Current through each resistor.
3. Total power consumed by the circuit.

4. - (PreLab) Calculation of Nominal Values of Figure #1

Given these values:

4A. Node Voltage Method
Use ORCAD to simulate the circuit of Figure #1.  Use the DC Bias Point analysis and get the dc values of currents and voltages in the circuit.  Use these dc values along with the general equations developed in sections 2 (node voltage analysis)  and calculate the nominal values of:

1. Voltage drop across each resistor.
2. Current through each resistor.
3. Total power consumed by the circuit.

4B. Nominal Values Using Mesh Current Method
Use the ORCAD simulation results of Figure #1 along with the general equations developed in sections 3 (mesh current analysis) and calculate the nominal values of:

1. Voltage drop across each resistor.
2. Current through each resistor.
3. Total power consumed by the circuit.

5. - Verification of Analysis for Figure #1

Construct the circuit of Figure #1.  Measure:

1. Voltage drop across each resistor.
2. Current through each resistor.
3. Total power consumed by the circuit.

                                   Figure #2
 

6. (PreLab) Maximum Power Transfer Analysis

In this section we will utilize the concept of maximum power transfer in Figure #2.  The aim is to transfer maximum power from the circuit to the load (RL).

1. Modify the circuit shown in Figure #2 to include the internal resistance of the voltage source (Rint).  Further modify the circuit to include the resistance burden (Rs) that would be caused by a current meter placed in series with RL.  Label this new circuit Figure #2A - Circuit with all major resistances shown.
2. Using the new circuit (Figure #2A), simplify the circuit of  in the left side of points a and b to its thevenin equivalent (leave RL in its original position). Develop a general equation that describes the maximum power to be transferred from the circuit to RL.

7. Calculation to find RL at Maximum Power Transfer

Use the following circuit specifications along with the general equation that you developed in Part 6 and find the value of RL that consumes maximum power from the circuit.

Circuit specifications for Figure #2A  (Notice values of  R1 and R2 are different from Figure 1)
R1 - 68 Ohm
R2 - 6.8 K Ohm
V1 = 1.5 Vdc
Assume Rint = 0 Ohm and Rs = 0 Ohm.
Label this RL as "RLcalculated with Rs=Rint=0"
 

8. Maximum Power Transfer Verification

Construct the circuit of Figure #2 using circuit specifications given in Part 7.
Follow these steps to measure RL:

1. Connect a current meter in series with RL so you can continously monitor the current through RL (IL).
2. Place a voltmeter across RL so you can constantly monitor the voltage across RL (VL).
3. Place a second voltmeter across R2 (V2).
4. Use 100 Ohm potentiometer as a RL in the circuit.  Vary RL and use MSExcel to key in the values of IL and VL as you vary RL. Calculate PL.  PL = I_L x V_L.

Place all measured data in Data Table 8 and plot the graph of PL vs RL (Graph of PL vs RL).
[Hint] RL can be calculated from the data V_L / I_L.

9.  Conclusions

1. Verify that the voltage burden caused by the current meter is within the manufacturer's specifications.
2. Compare the final measured value of RL (at PL_max) with the calculated value of section7.
3. Find the resistance burden (Rs) caused by the current meter from result of section 8.
4. Find the internal resistance of the power supply (Rint) using answer from section 8.