# Chapter 07 Series-Parallel Circuits

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The Series-Parallel Network Chapter 07Complex circuitsMay be separated both series and/or parallel elementsCombinations which are neither series nor parallel To analyze a circuitIdentify elements in series and elements in parallel Series-ParallelCircuitsSource:C-CTsaiFor example:R2, R3, and R4 are in parallel,Series with R1 and R5RT R1 (R2//R3//R4) R5Circuit Analysis: Theory and Practice Delmar Cengage LearningC-C TsaiThe Series-Parallel NetworkAnalysis of Series-Parallel CircuitsIn this circuit: R3 and R4 are in parallel Combination is in series with R2 Entire combination is in parallelwith R1Another example:C-C Tsai23Rules for analyzing series and parallel circuits apply: Same current occurs through all series elements Same voltage occurs across all parallel elements KVL and KCL apply for all circuitsSteps to simplify a circuit: Redraw complicated circuits showing the source at theleft-hand side and then label all nodes Simplify recognizable combinations of components Determine equivalent resistance RT and solve for thetotal current Label polarities of voltage drops on all components Calculate how currents and voltages split betweenelements in a circuit Verify your answer by taking a different approach4C-C Tsai1

Example: Analysis of Series-Parallel Circuits Example: Analysis of Series-Parallel CircuitsCombining R2 and R3 in parallelCircuit reduces to a series circuitUse Voltage Divider Rule to determine Vab and Vbc.Note that Vbc V2 is the voltage across R2 and R3Calculate all currents from Ohm’s Law.C-C TsaiFind the voltage Vab Redraw circuit in simple form Determined by combination of voltages across R1and R2 , or R3 and R4 (use voltage divider rule)5Example: Analysis of Series-Parallel CircuitsFind currents in the circuit First redraw the circuit and move source branch all the wayto left and reduce circuit to a series circuit Voltages: Use Ohm’s Law or Voltage Divider Rule Currents: Use Ohm’s Law or Current Divider RuleC-C Tsai7C-C Tsai6Example: Analysis of Series-Parallel CircuitsFind VabC-C Tsai82

Example: Bridge CircuitExample: Analysis of Series-Parallel CircuitsFind VabC-C Tsai 9Determine Vab and I if Rx is a short circuit (0 )Vab Va - Vb 8V – 0V 8VI 10 / [(50 200) // 5k] 10 / 238 42.2mAC-C TsaiBridge CircuitExample: Bridge Circuit Determine Vab and I if circuit has Rx 15 k Vab Va - Vb 8V – 7.5V 0.5VI 10 / [(50 200) // (5k 15k)] 10/247 40.5mAC-C Tsai10 11Determine Vab and I if Rx is openVab Va - Vb 8V – 10V -2VI 10 / (50 200) 10 / 250 40mAC-C Tsai123

*Transistor CircuitPotentiometersTransistor is a device that amplifies a signal Operating point of a transistor circuit is determined by adc voltage source Determine some dc voltages and currents Apply KVL: VBB RBIB VBE REIE Using IE 100IB, we find IB 14.3 A.C-C Tsai 13Potentiometers C-C Tsai14Load Effects of InstrumentsVbc changes Example of variable resistor used as potentiometerMoveable terminal is at uppermost positionthen Vbc 60 VAt the lowermost positionthen Vbc 0 VActual valueVR1 27V * 5M/(5M 10M) 9VIf load is added to circuit at upper positionthen Vbc 40 VAt the lower positionthen Vbc 0 VReading valueVR1 27V * 3.3M/(3.3M 10M) 6.75VLoading effect (9 - 6.75) / 9 25%C-C Tsai15C-C Tsai164

Example: Load Effects of InstrumentsExample: Load Effects of InstrumentsActual valueVR2 27V * 10M/(5M 10M) 18VI1 4mAI2 20mAIT 24mAReading valueVR2 27V * 5M/(5M 5M) 13.5VLoading effect (18 - 13.5) / 18 25%C-C Tsai17C-C TsaiGet RT Using MultisimCircuit Analysis Using MultisimUse Multisim to find the following quantities for thecircuit showna) Total resistance, RTb) Voltages V2 and V4c) Currents IT, I1, and I2C-C Tsai18 19Construct the circuit for determining the totalresistance RTC-C Tsai205

Get Voltages and currents UsingMultisimKernel abilities1. Can recognize which parts are in series or parallelfor a series-parallel circuit.2. Can compute the total resistance Rt of resistorsR1 Rn in series-parallel.3. Can recognize KVL and KCL for applying a seriesparallel circuit.4. Can recognize the voltage divider and current dividerfor applying a series-parallel circuit.5. Can recognize the loading effect for measuringvoltage and current.C-C Tsai2122Problem 35: Find EProblem 10: Find Rab and RbcC-C TsaiC-C Tsai23C-C Tsai246

Problem 37: Find the reading of ammeterC-C Tsai257

The Series-Parallel Network In this circuit: R 3 and R 4 are in parallel Combination is in series with R 2 Entire combination is in parallel with R 1 Another example: C-C Tsai 4 Analysis of Series-Parallel Circuits Rules for analyzing series and parallel circuits apply: Same current occurs through all series elements

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