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### lecture_10_Series___Parallel_1

Course: EEL 1001, Spring 2012
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voltage EET1015CDirectCurrentCircuits Lecture10 Prof.YingSong Review:ParallelCircuitsAnalysis The is the same across any component in the parallel circuit Vs = V1 = V2 = ... = VN Apply Ohm's law to find the current through each resistance. I1 = V1 R1 I2 = V2 R2 I3 = V3 R3 . Review:CurrentDivider Ix = Current through any branch: RT IT Rx R2 If only two=resistors in parallel: = I I I 1 R1 + R2...

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voltage EET1015CDirectCurrentCircuits Lecture10 Prof.YingSong Review:ParallelCircuitsAnalysis The is the same across any component in the parallel circuit Vs = V1 = V2 = ... = VN Apply Ohm's law to find the current through each resistance. I1 = V1 R1 I2 = V2 R2 I3 = V3 R3 . Review:CurrentDivider Ix = Current through any branch: RT IT Rx R2 If only two=resistors in parallel: = I I I 1 R1 + R2 T 2 R1 I T R1 + R2 Note: R1 + R2 on the denominator above is NOT the total resistance ! ComparisonofSeries&ParallelCircuits Series Circuits Parallel Circuits Current is the same everywhere. Voltage is the same every branch. Voltage divider: Rx Current divider:T R Vx = RT Vs V =0 N KVL @ a i =1 i loop: Total Resistance: Ix = Rx IT iN 1 I i = 0 = KCL@ a node: Total Resistance: Chap7:SeriesParallelCircuits Identifyingseriesparallelrelationships A series-parallel circuit consists of combinations of series connected and parallel connected components. R1 + R 2 || R 3 + represents series connection. NotationforSeriesParallelConnections R 4 + R1 + ( R 2 + R 5) || R 3 NotationforSeriesParallelConnections R1 + R 2 || R 3 + R 4 NotationforSeriesParallelConnections Label circuit node with letter or number will help you to redraw the circuit and identify the relationship. B B C A A C C D D R1 + R 2 || R 3 + R 4 || R 5 NotationforSeriesParallelConnections SeriesParallelCircuitsAnalysis There is no step-by-step procedure to follow for series-parallel circuits analysis, simply because of too many variations. Analysis tools Basic rules: Ohms Law, KCL, KVL Derived rules: voltage divider, current divider, total resistance for series connection, total resistance for parallel connection, etc. Often, figuring out the total resistance for seriesparallel circuit is a good point to start. TotalResistance(Steps) Indentify the series-parallel relationship Write down the series-parallel relationship with notations. Translate the notation into mathematically calculation. Replace Rx with the corresponding resistance value Replace + and || notation with the corresponding calculation . TotalResistance Relationship: R1 R + 2 || R 3 + R 4 Calculaiton: R 2 R3 RT = R1 + + R4 R 2 + R3 TotalResistance R1 + ( R2 + R3 ) || ( R4 || R5 + R6 ) R2+3 = R2 + R3 = 47 + 47 = 94 R4||5 = R4 R5 68g 39 = = 24.8 R4 + R5 68 + 39 R4||5+6 = R4||5 + R6 = 24.8 + 75 = 99.8 RT = 100 + 94 || 99.8 = 100 + 48.4 = 148.4 OnlinePractice TotalCurrent After getting RT, total current can be calculated using Ohms Law I = Vs T RT After that, circuit rules can be applied in any sequence to solve a circuit. Ohms Law KCL KVL Voltage divider Current divider Current is the same in series branch OhmsLawinSeriesParallel Ohms law can be applied to any scale as long as the subscripts match. Ohms Law on entire circuit:Vs = IT RT V1 = I1 R1 = IT R1 Ohms Law on a single component: Ohms Law on a branch: V2+3 = I 2+3 R2+3 KCL&KVLinSeriesParallelCircuits KVL can be applied to any CLOSED path. Vs = V1 + V2 + V3 KCL can be applied to any point in the circuit. I6 = I 4 + I5 VoltageDividerinSeriesParallelCircuits Voltage divider was defined on series circuits. To apply it to the series-parallel circuits, modification is needed: The voltage across any resistance in a series path is equal to the ratio of that resistance to the path's total resistance, multiplied by the voltage across the series path. Rx VX = V path R path VoltageDividerinSeriesParallelCircuits R2 V2 = V2+3 R2+3 CurrentDividerinSeriesParallelCircuits Current divider was defined on parallel circuits. To apply it to the series-parallel circuits, modification is needed: The current through any resistance in a parallel path is equal to the ratio of the path's total resistance to that resistance, multiplied by the total current of the parallel path. IX = R path Rx I path ACompleteExample V1 = Vs = 50 V (in parallel) I1 = V1 50V = = 89.3mA (Ohm's Law) R1 560 R2+3||4 = R2 + R3 || R4 = 330 + Vs is 50 V. I 2 = I 2+3||4 = V2+3||4 R2+3||4 = 330g 560 = 538 330 + 560 50V = 93mA (Ohm's Law) 538 Find out the voltage across I 2 = I 3 + I 4 =I 3||4 (KCL) and current through each resistor. R4 560 I3 = I 3||4 = 93mA = 58.5 mA (Current divider) R3 + R4 330 + 560 I 4 = I 2 I 3 =93 - 58.5 = 34.5 mA Find the rest voltages using Ohms Law
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