Series -Parallel Circuits - Oakton Community College

1 SeriesSeries-- parallel CircuitsParallel CircuitsTopics Covered in Chapter 66-1: Finding RTfor Series -Parallel Resistances6-2: Resistance Strings in parallel 6-3: Resistance Banks in Series6-4: Resistance Banks and Strings in Series -ParallelChapterChapter66 2007 The McGraw-Hill Companies, Inc. All rights Covered in Chapter 6 Topics Covered in Chapter 6 6-5: Analyzing Series -Parallel Circuits with Random Unknowns 6-6: The Wheatstone Bridge 6-7: Troubleshooting: Opens and Shorts in Series -Parallel CircuitsMcGraw-Hill 2007 The McGraw-Hill Companies, Inc. All rights : Finding 1: Finding RRTTfor for SeriesSeries-- parallel ResistancesParallel Resistances Overview of Series -Parallel Circuits A Series -Parallel circuit , or combination circuit , combines both Series and parallel connections. Most electronic Circuits fall into this Circuits are typically used when different voltage and current values are required from the same voltage source.

2 Series components form a Series string. parallel components form a parallel : Finding 1: Finding RRTTfor for SeriesSeries-- parallel ResistancesParallel Resistances Overview of Series -Parallel CircuitsThere are three branches in thiscircuit; sections 1and 2are Series : Finding 1: Finding RRTTfor for SeriesSeries-- parallel ResistancesParallel Resistances Overview of Series -Parallel CircuitsThere are three Series sections in thiscircuit; sections 1and 2are parallel : Finding 1: Finding RRTTfor for SeriesSeries-- parallel ResistancesParallel Resistances To find RTfor a Series -Parallel circuit , add the Series resistances and combine the parallel resistances. In this diagram, R1and R2are in Series , and R3and R4are in parallel . However, R2is not in Series with the parallel resistances: Resistances in Series have the same current, but the current in R2is equal to the sumof the branch currents I3and 6-1b: Schematic diagram of a Series -Parallel The McGraw-Hill Companies, Inc.

3 Permission required for reproduction or : Finding 1: Finding RRTTfor for SeriesSeries-- parallel ResistancesParallel Resistances For Fig. 6-1b, The Series resistances + = 1k The parallel resistances are:1k / 2 = The Series and parallel values are then added for the value of RT:1k + = k 66--2: Resistance Strings in Parallel2: Resistance Strings in parallel In this figure, branch 1 has two resistances in Series ; branch 2 has only one resistance. Ohm s Law can be applied to each branch, using the same rules for the Series and parallel components that were discussed in Chapters 4 and 5. Fig. 6-3a: Series string in parallel with another branch (schematic diagram).Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or : Resistance Strings in Parallel2: Resistance Strings in parallel Series circuit Current is the same in all components.

4 Vacross each Series Ris I R. VT= V1 + V2 + V3 +..+ etc. parallel circuit Voltage is the same across all branches. Iin each branch Ris V/R. IT= I1+ I2 + I3 +..+ : Resistance Strings in Parallel2: Resistance Strings in ParallelIis the samein the same across each parallel : Resistance Strings in Parallel2: Resistance Strings in parallel The current in each branch equals the voltage applied across the branch divided by the branch RT. The total line current equals the sum of the branch currents for all parallel strings. The RTfor the entire circuit equals the applied voltage divided by the total line current. For any resistance in a Series string, the IRvoltage drop across that resistance equals the string s current multiplied by the resistance. The sum of the voltagedrops in the Series string equals the voltage across the entire : Resistance Banks in Series3: Resistance Banks in Series In this figure, R2and R3are parallel resistances in a bank.

5 The parallel bank is in Series with R1. There may be more than two parallel resistances in a bank, and any number of banks in Series . Ohm s Law is applied to the Series and parallel components as seen 6-4a: parallel bank of R2and R3in Series with R1(Original circuit ).Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or : Resistance Banks in Series3: Resistance Banks in Series To find the total resistance of this type of circuit , combine the parallel resistances in each bank and add the Series =24V4AR=24V4A6 =10 (of R2+ R3)2 branches+ 1 (R1)6 = 5 + 1 66--4: Resistance Banks and Strings in 4: Resistance Banks and Strings in SeriesSeries--ParallelParallel To solve Series -Parallel (combination) Circuits , it is important to know which components are in Series with one another and which components are in parallel . Series components must be in one current path without any branch points.

6 To find particular values for this type of circuit , Reduce and combine the components using the rules for individual Series and parallel Circuits . Reduce the circuit to its simplest possible form. Then solve for the needed values using Ohm s : Resistance Banks and Strings in 4: Resistance Banks and Strings in SeriesSeries--ParallelParallel Example: Find all currents and voltages in Fig. 6-5. Step 1: Find RT. Step 2: Calculate main line current as IT= VT / RTFig. 6-5: Reducing a Series -Parallel circuit to an equivalent Series circuit to find the RT. (a) Actual circuit . (b) R3and R4in parallel combined for the equivalent The McGraw-Hill Companies, Inc. Permission required for reproduction or : Resistance Banks and Strings in 4: Resistance Banks and Strings in SeriesSeries--ParallelParallelFig. 6-5, cont. (c) RTand R6in Series added for R13. (d) R13 and R5in parallel combined for R18.

7 Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or : Resistance Banks and Strings in 4: Resistance Banks and Strings in SeriesSeries--ParallelParallelFig. 6-5e: The R18, R1, and R2in Series are added for the total resistance of 50 for The McGraw-Hill Companies, Inc. Permission required for reproduction or : Analyzing Series5: Analyzing Series -- parallel Circuits parallel Circuits with Random Unknownswith Random Unknowns In solving such Circuits , apply the same principles as before: Reduce the circuit to its simplest possible form. Apply Ohm s : Analyzing Series5: Analyzing Series -- parallel Circuits parallel Circuits with Random Unknownswith Random Unknowns Example: In Fig. 6-6, we can find branch currents I1and I2-3, and IT, and voltage drops V1, V2,and V3, without knowing the value of 6-6: Finding all the currents and voltages by calculating the branch currents The McGraw-Hill Companies, Inc.

8 Permission required for reproduction or : Analyzing Series5: Analyzing Series -- parallel Circuits parallel Circuits with Random Unknownswith Random Unknowns Find I1, I2-3, and 3AI1=90V30 ( parallel branches have the same voltage)6-5: Analyzing Series -Parallel Circuits with Random UnknownsI2-3=VRI2-3 = 2AI2-3=90V20 + 25 I2-3=90V45 IT= I1+ I2-3IT= 3A+ 2 AIT= 5A6-5: Analyzing Series -Parallel Circuits with Random Unknowns Find voltage drops V1, V2, and V3:Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or : Analyzing Series -Parallel Circuits with Random UnknownsV1= VA( parallel branches have the same voltage)V1= 90 VorV1= I1R1V2= I2-3R2V3= I2-3R3V1= 3A 30 V2= 2A(20 )V3= 2A(25 )V1= 90VV2= 40VV3= 50 VNote: V2+ V3= VA40V + 50V = 90V6-5: Analyzing Series -Parallel Circuits with Random Unknowns=RTITVA=RT5A90A18 =RT66--6: The Wheatstone Bridge6: The Wheatstone Bridge A Wheatstone bridge is a circuit that is used to determine the value of an unknown resistance.

9 The unknown resistor (RX) is in the same branch as the standard resistor (RS).Fig. 6-10: Wheatstone The McGraw-Hill Companies, Inc. Permission required for reproduction or : The Wheatstone Bridge6: The Wheatstone Bridge Resistors R1and R2form the ratio arm; they have very tight resistance tolerances. The galvanometer (M1), a sensitive current meter, is connected between the output terminals C and D. When R1 / R2= R3 / R4, the bridge is balanced. When the bridge is balanced, the current in M1is : The Wheatstone Bridge6: The Wheatstone Bridge Using a Wheatstone Bridge to Measure an Unknown Resistance RSis adjusted for zero current in When the current in M1= 0A, the voltage division between RXand RSis equal to that between R1and The McGraw-Hill Companies, Inc. Permission required for reproduction or : The Wheatstone Bridge6: The Wheatstone BridgeNote: When the Wheatstone bridge is balanced, it can be analyzed as two Series strings in parallel .

10 Note the following relationship:=RSRXR1R2=RXRS R1R266--7: Troubleshooting: Opens and 7: Troubleshooting: Opens and Shorts in SeriesShorts in Series -- parallel CircuitsParallel Circuits In Series -Parallel Circuits , an open or short in one part of the circuit changes the values in the entire circuit . When troubleshooting Series -Parallel Circuits , combine the techniques used when troubleshooting individual Series and parallel : Troubleshooting: Opens and 7: Troubleshooting: Opens and Shorts in SeriesShorts in Series -- parallel CircuitsParallel Circuits Effect of a Short in a Series -Parallel circuit The total current and total power 6-13: Effect of a short circuit with Series -Parallel connections. (a) Normal circuit with S1open. (b) circuit with short between points A and B when S1is closed; now R2and R3are The McGraw-Hill Companies, Inc. Permission required for reproduction or : Troubleshooting: Opens and 7: Troubleshooting: Opens and Shorts in SeriesShorts in Series -- parallel CircuitsParallel Circuits Effect of a Short in a Series -Parallel CircuitCopyright The McGraw-Hill Companies, Inc.