Lesson 18: Series-Parallel AC Circuits

1. Lesson 18: Series-Parallel AC Circuits

2. Learning Objectives • Compute the total impedance for AC series-parallel circuits. • Apply Ohm’s Law, Kirchhoff’s Voltage Law, voltage divider rule, Kirchhoff’s Current Law, and current divider rule to AC series parallel networks and its elements. • Solve AC series parallel networks.

3. Common Mistakes in AC analysis • Confusing XC and C or XLand L. • Confusing ω and f when calculating XC and XL. • Using VPK and IPK in phasors. • Using VRMS and IRMS in time domain. • Incorrectly converting from rectangular to polar forms. • Losing track of signs when adding up impedances.

4. Impedance and AC Circuits Solution steps: • Transform time domain currents and voltages into phasors. • Calculate impedances for circuit elements. • Perform all calculations using complex math. • Transform resulting phasors back to time domain (if reqd).

5. Series-Parallel Rules for AC Circuits Similar to DC circuits we can apply the following rules to the AC series-parallel circuit, remembering that we are using impedances (Zx) instead of pure resistance: • Ohm’s Law: • VDR: • CDR: STILL TRUE: KVL: E = V1 + V2 + V3 STILL TRUE: KCL: IT = I1 + I2 + I3

6. Common Mistakes Applying Ohm’s Law • Incorrectly calculating voltage drop or current direction across an impedance. • GIVEN: Vb=361-174⁰V • FIND: IL Using Nodal Analysis: IL

7. Common Mistakes Applying VDR Using wrong “ZTOT”. ZTOT in the VDR equation refers to just the combination of the impedances resistors that are in serieswith each other. • Confusing E and Vcn. • E in the VDR is the voltage drop across those impedances in series. Vcn does NOT equal E

8. Common Mistakes Applying CDR Using ZTOT in the CDR instead of ZEQfor the impedance of the parallelbranches. • Not using ALL the series impedances in a branch.

9. Example Problem 1: Series/Parallel AC Using CDR: Find I1and I2. Using KCL:

10. Example Problem 2: Series/Parallel AC Find VR, IC , ILand IR. e(t)=169.7 sin (ωt)

11. Example Problem 3 Assume this is a phasor Find I2and VL.

12. Example Problem 4 Find VRusing the Voltage Divider Rule. WRONG! Don’t do this!! Common mistake #1 mentioned earlier. Remember, we need to account for the voltage drop across R1, so:

13. Example Problem 5 Find I2using the Current Divider Rule. Find Va and Vac.

14. Example Problem 6 Compute Vab. Vc

15. QUESTIONS?