Lesson 22
Series/Parallel AC
Circuits
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.
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
REVIEW
Impedance and AC Circuits

Solution technique
1.
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)
2.
3.
4.
Example Problem 1: Series AC
Find ZT, VR, I & i
Example Problem 2: Parallel AC
a. Find the total impedance ZT.
b. Calculate and graph E, IC, IR, IL
ITOT  4.1753.13 A
Example Problem 2
Common Mistakes Applying Ohm’s Law

Incorrectly calculating voltage drop or current direction
across an impedance

GIVEN: Vb=361-174V
REQD: IL
SOLN:


 Vb  Va
IL  
 ZL
  361  174   1200 


490
 

Example Problem 3: Series/Parallel
Find I1 and I2
Example Problem 4: Series/Parallel
Find VR, IC , IL and IR
e(t)=169.7 sin (ωt)
Example Problem 5
Find I2 and VL
Common Mistakes Applying VDR
 Zx 
Vx  E 

 ZTOT 

#1: Confusing E and Vcn

E in the VDR is the voltage drop across those impedances in
series.
Vab  ?????????
ZTOT  Z R1  ZC  Z R 2
 ZC 
Vab  Vcn 

 ZTOT 
Common Mistakes Applying VDR
 Zx 
Vx  E 

 ZTOT 

#2: Using wrong “ZTOT”

ZTOT in the VDR equation refers to just the combination of the
impedances resistors that are series with each other.
Vab  ?????????
ZTOT  Z R1  ZC  Z R 2
 ZC 
Vab  Vcn 

 ZTOT 
Example Problem 6
Find VR using the Voltage Divider Rule
 Z EQ 
Common Mistakes Applying CDR I x  ITOT 

 Zx 
 #1: Using ZTOT in the CDR instead of ZEQ for the
impedance of the parallel branches.
I 2  ?????????
Z EQ  Z L  Z R1  Z C  Z R 2 
I 2  ITOT
Z EQ




  Z R1  ZC  Z R 2  
Common Mistakes Applying CDR I x  ITOT

 Z EQ 


 Zx 
#2: Not using ALL the series impedances in a
branch
I 2  ?????????
Z EQ  Z L  Z R1  Z C  Z R 2 
I 2  ITOT
Z EQ




  Z R1  ZC  Z R 2  
Example Problem 7
Find I2 using the Current Divider Rule. Find Va and Vac.
Example Problem 8
Compute Vab.
Example Problem 9
Use the Current Divider Rule to find I3