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

8. Common Mistakes Applying CDR
Using ZTOT in the CDR instead of ZEQ for the impedance of the parallel branches.
Not using ALL the series impedances in a branch.

9. Example Problem 1: Series/Parallel AC
Find I1 and I2.
Using CDR:
Using KCL:

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

11. Example Problem 3
Find I2 and VL.
Assume this is a phasor

12. Example Problem 4 Find VR using 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 I2 using the Current Divider Rule. Find Va and Vac.

14. Example Problem 6
Compute Vab. Vc

15. QUESTIONS?