Equipment:
List the equipment that you will use for this experiment.
 

Components:

• R1 - 68 K Ohm Resistor
• R2 - 62 Ohm Resistor
• R3 - 6.2 K Ohm Resistor
• R4 - 62 K Ohm Resistor
• R5 - 620 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.

1. - Keithley Model 175 - Maximum Voltage Across An Unknown

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)  620 Ohm
2)  6.2 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 that will give you:
 

1. Voltage drop across each resistor.  Here is the hypothetical example:

The voltage drop across R4:      Equation #1:      VR4 = IR4 x R4
 
2. Current through each resistor.  Here is the hypothetical example:

The current across R1:      Equation #2:      IR1 = (V1-V3) / R1
 
3. Total power consumed by the circuit.  Here is the hypothetical example:
4. The power that the circuit dissipates:      Equation #3:      Pcircuit = (Ickt)² x Rcircuit

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

Calculate the nominal values of voltages, currents and power dissipation using:
 

4A. Node Voltage Method
Use the general equations developed in sections 2 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 general equations developed in sections 3 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.
1. Current through each resistor.
2. 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.

1. 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.

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
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 (V₂) across R2 so you can accurately monitor the voltage applied to the circuit.
4. Vary RL and use MSExcel to key in the values of IL and VL as you vary RL. Calculate PL.
5. When maximum PL is found, disconnect V1 from the circuit and measure RL as accurately as possible.

Place all measured data in Data Table 8.
 

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 with the calculated value of section7.
3. Find the internal resistance of the power supply (Rint).
4. Find the resistance burden (Rs) caused by the current meter.