lesson 22 series/parallel ac circuits. learning objectives determine total impedance of ac parallel...
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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