1. Lesson 22 Series/Parallel AC Circuits

2. Learning Objectives
Determine total impedance of AC parallel and series 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
Loosing track of signs when adding up impedances

4. Impedance and AC Circuits
REVIEW
Impedance and AC Circuits
Solution technique
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. Example Problem 1: Series AC
Find ZT, VR, I & i

6. Example Problem 2: Parallel AC
Find the total impedance ZT.
Calculate and graph E, IC, IR, IL

7. Example Problem 2

8. Common Mistakes Applying Ohm’s Law
Incorrectly calculating voltage drop or current direction across an impedance
GIVEN: Vb=361-174V
REQD: IL
SOLN:

9. Example Problem 3: Series/Parallel
Find I1 and I2

10. Example Problem 4: Series/Parallel
Find VR, IC , IL and IR
e(t)=169.7 sin (ωt)

11. Example Problem 5
Find I2 and VL

12. Common Mistakes Applying VDR
#1: Confusing E and Vcn
E in the VDR is the voltage drop across those impedances in series.

13. Common Mistakes Applying VDR
#2: Using wrong “ZTOT”
ZTOT in the VDR equation refers to just the combination of the impedances resistors that are series with each other.

14. Example Problem 6
Find VR using the Voltage Divider Rule

15. Common Mistakes Applying CDR
#1: Using ZTOT in the CDR instead of ZEQ for the impedance of the parallel branches.

16. Common Mistakes Applying CDR
#2: Not using ALL the series impedances in a branch

17. Example Problem 7
Find I2 using the Current Divider Rule. Find Va and Vac.

18. Example Problem 8
Compute Vab.

19. Example Problem 9
Use the Current Divider Rule to find I3