CHAPTER 9 Series Parallel Analysis of AC Circuits …

1 Contemporary Electric Circuits , 2nd ed., Prentice-Hall, 2008 Class Notes Ch. 9 Page 1 Strangeway, Petersen, Gassert, and Lokken CHAPTER 9 Series Parallel Analysis of AC Circuits CHAPTER Outline AC Series Circuits AC Parallel Circuits AC Series Parallel Circuits Analysis of Multiple-Source AC Circuits Using Superposition AC Series Circuits In DC Analysis of Series - Parallel Circuits , what type of numbers was utilized? _____ If the signal source is AC instead of DC and the circuit contains inductors and/or capacitors, what type of numbers would you expect to be utilized? Why? Good news: the circuit Analysis techniques are the same. What is the phase shift of the voltage with respect to the current for an inductor?

2 _____ Why? What is the phase shift of the voltage with respect to the current for a capacitor? _____ Why? What is the phase shift of the voltage with respect to the current for a resistor? _____ Why? What would you expect the phase shift to be for AC signals in Series , Parallel , and Series Parallel Circuits with resistances, inductors, and capacitors? Why? Contemporary Electric Circuits , 2nd ed., Prentice-Hall, 2008 Class Notes Ch. 9 Page 2 Strangeway, Petersen, Gassert, and Lokken How is Series Parallel circuit Analysis with AC sources approached? Review the circuit laws, concepts, and re-sults for DC circuit Analysis by stating in words each relation that follows: 1. I1 = I2 = I3 = . = IN _____ ( ) 2.

3 Rise1rise2rise3drop1drop2drop310 NnnVVVVVVV _____ ( ) How are the signs for voltage rises and voltage drops assigned (Figure below)? Is the key to the sign of the voltage rise (or drop) the current direction or the direction that KVL is applied? 3. 1231 NTNnnRRRRRR _____ ( ) 4. xxTTRVVR _____ ( ) Which of these laws and concepts are applicable to AC Series Circuits ? Answer the following questions: Does constant current throughout a Series circuit change for any signal? _____ Does KVL change for any signal? Why or why not? _____ Are 3 and 4 above valid? Why or why not? _____ If the same DC circuit Analysis techniques are valid for AC, and resistances are used in DC circuit Analysis , then what must be used in AC circuit Analysis ?

4 Why? State in words the circuit laws, concepts, and results for AC Series Circuits : 1. 123 NIIII _____ ( ) 2. rise1rise2rise3drop1drop2drop310 NnnVVVVVVV _____ ( ) Contemporary Electric Circuits , 2nd ed., Prentice-Hall, 2008 Class Notes Ch. 9 Page 3 Strangeway, Petersen, Gassert, and Lokken How is a voltage polarity assigned with AC signals considering the polarity is alternating? 3. 1231 NTNnnZZZZZZ _____ ( ) 4. xxTTZVVZ _____ ( ) Example (Explain each step.) For the circuit shown in Figure below, determine (a) ,TZ (b) ,I (c) RV and LV by the VDR, and (d) CV by Ohm s law. (e) Verify KVL. _____: vS(t) = 10 sin(827t) V R = 35 C = 20 F L = 100 mH _____: a.

5 TZ b. I c. RV and LV by VDR d. CV by Ohm s law e. Verify KVL Strategy: Determine ,,RLZZ and CZ TRCLZZZZ Label a circuit diagram with voltage polarities and current directions. ,STRLRSLSTTCCVIZZZVVVVZZVI Z 0 SRCLVVVV Solution: 35 RZR Contemporary Electric Circuits , 2nd ed., Prentice-Hall, 2008 Class Notes Ch. 9 Page 4 Strangeway, Petersen, Gassert, and Lokken (827)(20 )CZjjjC (827)( ) Ljj a. Note: All voltages and currents are expressed as peak values in this example. See Figure below. b. 10 c. 3510 Determine LV in a similar manner.

6 Answer: VLV d. ( )( )CCVI Zj V e. (Refer to Figure ) 0 SRCLVVVV Perform KVL. Is KVL satisfied? Contemporary Electric Circuits , 2nd ed., Prentice-Hall, 2008 Class Notes Ch. 9 Page 5 Strangeway, Petersen, Gassert, and Lokken AC Parallel Circuits State the important laws, concepts, and results that were found for DC Parallel Circuits in words: 1. VS = V1 = V2 = V3 = = VN _____ ( ) 2. 12310 NnNnIIIII _____ ( ) How is the sign of the current assigned to if it is entering the node? Leaving the node? 3. 121111 TNRRRR _____ in general ( ) 121212 TRRRR RRR _____for two Parallel resistors ( ) 4.

7 TTxxIRIR _____ in general ( ) 21121212 , TTI RI RIIRRRR _____for two Parallel resistors ( ) 5. 1 IGVR _____ ( ) 6. GT = G1 + G2 + . + GN _____ ( ) Which of these laws and concepts are applicable to AC Series Circuits ? Answer the following questions: Does constant voltage across a Parallel circuit change for any signal?_____ Does KCL change for any signal? Why or why not?_____ Are 3 - 6 above valid? Why or why not?_____ If the same DC circuit Analysis techniques are valid for AC, and resistances are used in DC circuit Analysis , then what must be used in AC circuit Analysis ? Why? Contemporary Electric Circuits , 2nd ed., Prentice-Hall, 2008 Class Notes Ch. 9 Page 6 Strangeway, Petersen, Gassert, and Lokken State in words the circuit laws, concepts, and results for AC Parallel Circuits : 1.

8 123 SNVVVVV _____ ( ) 2. 12310 NnNnIIIII _____ ( ) 3. 121111 TNZZZZ (general or special case?) _____ ( ) 121212 TZZZZ ZZZ (general or special case?) _____ ( ) 4. TTxxIZIZ (general or special case?) _____ ( ) 21121212 , TTI ZI ZIIZZZZ (general or special case?) _____ ( ) Example (Explain each step.) For the circuit shown in Figure below, determine (a) ,TZ (b) ,V (c) RI by the CDR, and (d) CI by Ohm s law. (e) Verify KCL. _____: R = 10 XC = 18 820 ATI _____: a. TZ T b. V c. RI by the CDR d. CI by Ohm s law e. Verify KCL _____: Determine RZ and CZ RCTRCZZZZZ Label a circuit diagram with voltage polarities and current directions.

9 TTVI Z (which equation is easier? ornote the previous step)TCTTRRRRCIZIZIIZZZ Contemporary Electric Circuits , 2nd ed., Prentice-Hall, 2008 Class Notes Ch. 9 Page 7 Strangeway, Petersen, Gassert, and Lokken CCVIZ Apply KCL to the top node. Solution: 10 RZR 18 CCZjXj a. (10)( 18) b. See Figure below for voltage polarity and current direction assignments. (820 )( ) VTTVI Z c. (820 )( )10 TTRRIZIZ A d. A18 CCVIjZ e. KCL at _____ node: 0 TRCIII Perform KCL: Is KCL satisfied? Contemporary Electric Circuits , 2nd ed., Prentice-Hall, 2008 Class Notes Ch. 9 Page 8 Strangeway, Petersen, Gassert, and Lokken What is the inverse of resistance (G = 1/R)?

10 _____ What is the inverse of reactance? 1BX _____ ( ) Identify: 1 LLBX _____ 1 CCBX _____ ( ) If susceptance is the inverse of reactance, what is the inverse of impedance? _____ 1YZ ( ) Is Y a complex number? Why or why not? _____ How does admittance ()Y relate to conductance (G) and susceptance (B)? Explain each step: ZRjX _____ ( ) Why is the plus sign used with inductive reactance?_____ Why is the minus sign used with capacitive reactance? _____ YGjB _____ ( ) Conductance is the _____ part of admittance and susceptance is the _____ part of admittance. 1()IVIIYVZV _____ ( ) Why is the sign minus used with inductive susceptance?_____ Why is the plus sign used with capacitive susceptance? _____ What is the unit of admittance?