Lesson 22Series/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

Impedance and AC Circuits

Solution technique1. Transform time domain currents and voltages into phasors

2. Calculate impedances for circuit elements

3. Perform all calculations using complex math

4. Transform resulting phasors back to time domain (if reqd)

REVIEW

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

4.17 53.13 ATOTI

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:

361 174 120 0

4 90b a

LL

V VI

Z

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

#1: Confusing E and Vcn

E in the VDR is the voltage drop across those impedances in series.

1 2TOT R C R

Cab cn

TOT

Z Z Z Z

ZV V

Z

?????????abV

xx

TOT

ZV E

Z

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.

1 2TOT R C R

Cab cn

TOT

Z Z Z Z

ZV V

Z

?????????abV

xx

TOT

ZV E

Z

Example Problem 6

Find VR using the Voltage Divider Rule

Common Mistakes Applying CDR

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

1 2

21 2

EQ L R C R

EQTOT

R C R

Z Z Z Z Z

ZI I

Z Z Z

2 ?????????I

EQx TOT

x

ZI I

Z

Common Mistakes Applying CDR

#2: Not using ALL the series impedances in a branch

1 2

21 2

EQ L R C R

EQTOT

R C R

Z Z Z Z Z

ZI I

Z Z Z

2 ?????????I

EQx TOT

x

ZI I

Z

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