1. EE188L EE I Laboratory Lab #4 KVL, KCL and Nodal Analysis

2. Lab #3 Overview First Week Simulation using MultiSim (see Multisim.ppt) Wye-Delta calculations Activity #2 – Build circuit Measure voltages, calculate currents Verify KVL (through step 10 of Activity #2) Second Week Activity #2 – Build same circuit Verify KCL Change source voltage Activity #3 – Modify circuit using Delta-Wye Nodal Analysis Calculations

3. Multisim Window

4. Delta or  Wye or Y Wye-Delta Transformation Y to Δ Equations Δ to Y

5. Kirchhoff’s Voltage Law, KVL Loop (0, 1, 2, 0) V 0,1 + V 1,2 + V 2,0 = 0 V -3 V + V R1 - V R3 = 0 V Loop (0, 3, 2, 0) V 0,3 + V 3,2 + V 2,0 = 0 V V R4 + V R2 - V R3 = 0 V For example: V 1,2 = - V 2,1 = V R1

6. Nodal Analysis 1 A current is entering the node if the current is leaving the device. A current is leaving the node if the current is entering the device.

7. Nodal Analysis 2 Apply Ohm’s Law (I = V/R) for R 1 : current entering node 2 = (V 1 - V 2 ) / R 1 current leaving node 2 = (V 2 - V 1 ) / R 1

8. Kirchhoff’s Current Law, KCL KCL at node 2: Shade indicates a node At node 1, V 1 =3 v. due to source At node 0, V 0 =0 v. due to ground KCL at node 3:

9. Nodal Analysis Shade indicates a node Substitute the known voltages into the equations that were obtained at nodes 2 & 3 Solve the two equations for V2 and V3 You can put the two equations in matrix form and solve using Matlab or any mathematics program (or your calculator).