The George Washington University
School of Engineering and Applied Science
Department of Electrical and Computer Engineering
ECE 11 - Fall 2003

Experiment # 2

DC Series and Parallel Circuits

Equipment:
2 Keithley Model 175 Digital Multimeter (DMM)
2 Pair of Banana to mini-grabber test leads
1 Agilent E3631A Triple Output DC Power Supply

Components:

• R1 - 470 Ohm Resistor
• R2 - 560 Ohm Resistor
• R3 - 680 Ohm Resistor
• R4 - 750 Ohm Resistor
• R5 - 820 Ohm Resistor
• R6 - 1 K Ohm Resistor
Objectives:
• Determine the value of resistors according to their color codes.
• Measure the value of resistors with an Ohm Meter.
• Connect electronic components in series or parallel combination on your solderless bread board.
• Measure the total resistance in a series/parallel circuit.
• Calculate the equivalence resistance in a series/parallel circuit using nominal and measured values.
• Calculate the total current in a series/parallel circuit for a given applied voltage.
• Calculate the voltage drop across all components in a series/parallel circuit.
• Calculate the expected total power dissipated in a series/parallel circuit from nominal and measured values.
• Set the voltage on a power supply.
• Limit the current on a power supply.
• Make power supply connections to a circuit.
• Measure the actual voltage drop across all components.
• Measure the actual current through each component.
• Find the actual power dissipated in each component of a series/parallel circuit.
• Create a data table.
• Experience the limit of the DMM.

1.- DC Power Supply Set tup

In this section you will learn in detail on how to supply voltage and current to your circuit using power supply equipment available in the lab.
Consult the instruction manual for the Agilent E3631A Triple Output DC Power Supply and explain, step by step with a block diagrams if necessary:

1.How would you set the power supply to get a 3.6V  voltage.  Use DMM to verify the voltage.
2. How to limit the current to 100mA  Use DMM to verify the current limit.

Figure 1A

Figure 1B

Figure 1C

2.- (PreLab H/W) Equivalence DC Resistance

Based on the class notes, you should be familiar with the concept of resistors in series and resistors in parallel.  In this section you are asked to simplify circuits given to find their equivalence resistance.

1. DERIVE an equivalence DC resistance (Reqv) general formula for circuit of Figure 1A.   DO NOT substitute values into the resistors yet.  Leave the resistors in their reference designator symbol.  Show the detail steps on how you simplify the circuit and finally give the final formula of the Reqv of Figure 1A.
2. DERIVE an equivalence DC resistance (Reqv) general formula for circuit of Figure 1B.   DO NOT substitute values into the resistors yet.  Leave the resistors in their reference designator symbol.  Show the detail steps on how you simplify the circuit and finally give the final formula of the Reqv of Figure 1B.
3. DERIVE an equivalence DC resistance (Reqv) general formula for circuit of Figure 1C.   DO NOT substitute values into the resistors yet.  Leave the resistors in their reference designator symbols.  Show the detail steps on how you simplify the circuit and finally give the final formula of the Reqv of Figure 1C.  [Hint] You will have to do some transformation to simplify the circuit.

3. - (PreLab H/W) DC Calculations

In this section you will do some ORCAD simulation and mathematic calculation to find voltage, current and power dissipation of each resistor in the three circuits  given.  In the simulation, use nominal values of resistors given in the component section of this report.  Use V1 = 3.6 Vdc.

3A. For the circuit of Figure 1A:

1. Calculate the equivalent resistance (Reqv).
2. Find the expected voltage drop across each resistor.
3. Find the expected current through each resistor.
4. Find the total current(Itotal).
5. Calculate the power dissipated by each resistor.
6. Create Data Table 3A - Calculated Values of Figure 1A with the above information in it.
3B. For the circuit of Figure 1B:
1. Calculate the equivalent resistance (Reqv).
2. Find the expected voltage drop across each resistor.
3. Find the expected current through each resistor.
4. Find the total current(Itotal).
5. Calculate the power dissipated by each resistor.
6. Create Data Table 3B - Calculated Values of Figure 1B with the above information in it.
3C. For the circuit of Figure 1C:
1. Find the equivalent resistance (Reqv).
2. Find the expected voltage drop across each resistor.
3. Find the expected current through each resistor.
4. Find the total current(Itotal).
5. Calculate the power dissipated by each resistor.
6. Create Data Table 3C - Calculated Values of Figure 1C with the above information in it.

7.
4. - DC Measurement

In this section you will construct the circuits of Figure 1A, Figure 1B and Figure 1C.  You will then do some detailed measurement to find voltage, current and power dissipation of each resistor in the three circuits  given.  Use V1 = 3.6 Vdc.

4A. For the circuit of Figure 1A:

1. Construct the circuit of Figure 1A.  DO NOT connect the power supply (V1) to the circuit yet.  Use DMM to measure the equivalent resistance (Reqv) of Figure 1A.
2. Connect the power supply (V1=3.6 Vdc) to the circuit.  Use DMM to measure the  voltage drop across each resistor.
3. Use DMM to measure the current through each resistor in the circuit.
4. Measure the total current(Itotal) used by circuit.
5. Calculate the power dissipated by each resistor.
6. Create and complete Data Table 4A - Measured Values of Figure 1A with the above information in it.

4B. For the circuit of Figure 1B:

1. Construct the circuit of Figure 1B.  DO NOT connect the power supply (V1) to the circuit yet.  Use DMM to measure the equivalent resistance (Reqv) of Figure 1B.
2. Connect the power supply (V1=3.6 Vdc) to the circuit.  Use DMM to measure the voltage drop across each resistor.
3. Use DMM to measure the current through each resistor in the circuit.
4. Measure the total current(Itotal) used by circuit.
5. Calculate the power dissipated by each resistor.
6. Create and complete Data Table 4B - Measured Values of Figure 1B with the above information in it.

4C. For the circuit of Figure 1C:

1. Construct the circuit of Figure 1C.  DO NOT connect the power supply (V1) to the circuit yet.  Use DMM to measure the equivalent resistance (Reqv) of Figure 1C.
2. Connect the power supply (V1=3.6 Vdc) to the circuit.  Use DMM to measure the voltage drop across each resistor.
3. Use DMM to measure the current through each resistor in the circuit.
4. Measure the total current(Itotal)  used by circuit.
5. Calculate the power dissipated by each resistor.
6. Create and complete Data Table 4C - Measured Values of Figure 1C with the above information in it.

5.- Design, Build and Test the Voltage Ladder

In this section, you are asked to design a voltage ladder using the concept of Voltage Divider.  Use circuit of Figure 1A and find the appropriate values of R1, R2, R3 and R4 to build a voltage ladder with the following specifications:

Total Power Consumed (Ptotal): < 0.18 Wdc
Power Supply (V1) : 12 Vdc + 5%
VAB: 1.5 Vdc + 5%
VBC: 2.5 Vdc + 5%
VCD: 3.5 Vdc + 5%
VDE: 4.5Vdc + 5%
All resistance must be greater than 100 Ohm.

Find the node voltages associated with A, B, C, D and E.
Test your circuit and check whether the specification is satisfied.

6.  Conclusions

1. Compare the calculation results from section 3 to measurement results from section 4 on the circuits of Figure 1A, 1B and 1C.  If there are differences between the calculated and measured results, include a discussion on why the differences happen..
2. Explain the concept of tolerance in all the devices and equipment and how to get around the problem of inaccurate measurement.
Modified to HTML format by Faisal Mohd Yasin, cepus@seas.gwu.edu, Sept. 2001.
Modified by Yang Cao, ycao@gwu.edu, Sept. 2003