Circuit calculations: Node-Voltage and Mesh-Current We continue our study of some simple and representative circuits as we develop and practice our understanding of basic circuit analysis techniques. Below are three circuits. You should calculate the node voltage for circuits 1-2, the mesh currents for the same circuits and then use superposition to find the resistor voltage for circuit 3. The measurements will be quite easy you can probably complete all the bench work in an hour or so, if you are proficient at building and measuring the circuits. Note that the circuits use the same 5 or 6 resistors over and over. Be sure to measure and record the exact resistor values. In lab, build each circuit using the DC supplies in the lab and resistors from your component bag. 1. The node-voltage method Analyze circuits 1 2 using the node-voltage method. Build each of the following two circuits, and apply the described DC voltages. Choose one node for ground and then identify all of the other unknown nodes. Use the voltmeter to measure the node voltages with respect to your chosen ground. (If you do not yet know how to choose a ground and identify the unknown nodes, then measure the voltages across each of the resistors. This will allow you to calculate the node voltages later.) V S Figure 1. The first circuit. For the circuit shown above, VS = 10 VDC, R1 = 1 kω, R2 = 1.5 kω, R3 = 2.2 kω, R4 = 3.3 kω, and R5 = 4.7 kω. 1
R 2 + VS Figure 2. The second circuit. For the circuit shown above, Vs = 5 V. The resistors are R1 = 1 kω, R2 = 1.5 kω, R3 = 2.2 kω, R4 = 3.3 kω, R5 = 4.7 kω. 2. The mesh-current method Analyze the following two circuits using the mesh-current method. In lab, build each circuit and apply the described DC voltages. Identify each of the mesh currents in the circuit. For the individual meshes, insert the ammeter to measure the mesh currents. Be sure to insert the ammeter into a branch where you will measure only one mesh current do not use branches where two mesh currents are flowing. (If you do not yet know how to identify mesh currents and which branches have only a single mesh current flowing prior to lab time, then measure the voltages across each of the resistors in the circuit. This will allow you to calculate the mesh currents later.) V S Figure 1. The first circuit. For the circuit shown above, VS = 10 VDC, R1 = 1 kω, R2 = 1.5 kω, R3 = 2.2 kω, R4 = 3.3 kω, and R5 = 4.7 kω. 2
R 2 + VS Figure 2. The second circuit. For the circuit shown above, Vs = 5 V. The resistors are R1 = 1 kω, R2 = 1.5 kω, R3 = 2.2 kω, R4 = 3.3 kω, R5 = 4.7 kω. 3
3. Superposition Analyze the circuits below using the superposition method to find the voltages across each resistor. In lab, build each circuit and apply the DC voltages. Use the voltmeter to measure the voltage across each resistor in the circuit. Then, use superposition at the lab bench. For the first circuit, remove VS2 and replace it with a short circuit. (Remove the source before inserting the short circuit wire.) Measure all of the resistor voltages with only VS1 powering in the circuit. Then remove VS1, replacing it with a short circuit. Finally remove the short circuit from the other side and put VS2 back in place. Measure the resistor voltages again. Of course, the sum of the two partial measurements should add to the total resistor voltages measured above when both sources were in place. When measuring the partial voltages, be sure to measure the resistors with the same polarity each time. V S1 + VS2 Figure 3. The first superposition circuit. For the circuit shown above, VS1 = 10 V, VS2 = 5 V, R1 = 1 kω, R2 = 1.5 kω, R3 = 2.2 kω, R4 = 3.3 kω, and R5 = 4.7 kω. Use the +20-V supply for VS1 and the +6-V supply for VS2. Be sure to connect both negative supply terminals to the circuit ground 4
4. Clean up Once you have finished all of your lab work, be sure to: put all of your components back in component bins, return all of the wires to the wire rack on the wall, turn off all of the equipment, and clean up any debris that is on your work bench. Reporting Prepare a report discussing your calculations and measurements for the three methods. The main body of the report does not need to be long. Mostly it will be series of tables comparing calculated and measured values. Be sure to note and comment on any differences between the calculations and measurements. Of course, the appendix containing all of the calculations will be lengthy. Both lab partners must work together to complete all of the calculations. 5