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RESISTIVE CIRCUITS • SERIES/PARALLEL RESISTOR COMBINATIONS - A TECHNIQUE TO REDUCE THE COMPLEXITY OF SOME CIRCUITS • LEARN TO ANALYZE THE SIMPLEST CIRCUITS • THE VOLTAGE DIVIDER • THE CURRENT DIVIDER • WYE - DELTA TRANSFORMATION - A TECHNIQUE TO REDUCE COMMON RESISTOR CONNECTIONS THAT ARE NEITHER SERIES NOR PARALLEL SERIES PARALLEL RESISTOR COMBINATIONS UP TO NOW WE HAVE STUDIED CIRCUITS THAT CAN BE ANALYZED WITH ONE APPLICATION OF KVL(SINGLE LOOP) OR KCL(SINGLE NODE-PAIR) WE HAVE ALSO SEEN THAT IN SOME SITUATIONS IT IS ADVANTAGEOUS TO COMBINE RESISTORS TO SIMPLIFY THE ANALYSIS OF A CIRCUIT NOW WE EXAMINE SOME MORE COMPLEX CIRCUITS WHERE WE CAN SIMPLIFY THE ANALYSIS USING THE TECHNIQUE OF COMBINING RESISTORS… … PLUS THE USE OF OHM’S LAW SERIES COMBINATIONS PARALLEL COMBINATION G p G1 G2 ... GN FIRST WE PRACTICE COMBINING RESISTORS 3k SERIES 6k||3k (10K,2K)SERIES 6k || 12k 4k 5k 3k 12k EXAMPLES COMBINATION SERIES-PARALLEL 9k If the drawing gets confusing… Redraw the reduced circuit and start again 18k || 9k 6k RESISTORS ARE IN SERIES IF THEY CARRY EXACTLY THE SAME CURRENT 6k 6k 10k RESISTORS ARE IN PARALLEL IF THEY ARE CONNECTED EXACTLY BETWEEN THE SAME TWO NODES EFFECT OF RESISTOR TOLERANCE NOMINAL RESISTOR VALUE : 2.7k RESISTOR TOLERANCE : 10% RANGES FOR CURRENT AND POWER? 10 NOMINAL CURRENT : I 3.704 mA 2.7 10 2.7 _ 37.04 mW 10 3.367 mA MINIMUM POWER(VImin ) : 33.67 mW 1.1 2.7 10 4.115 mA MAXIMUM POWER : 41.15 mW 0.9 2.7 MINIMUM CURRENT : I min MAXIMUM CURRENT : I max NOMINAL POWER : P 2 CIRCUIT WITH SERIES-PARALLEL RESISTOR COMBINATIONS THE COMBINATION OF COMPONENTS CAN REDUCE THE COMPLEXITY OF A CIRCUIT AND RENDER IT SUITABLE FOR ANALYSIS USING THE BASIC TOOLS DEVELOPED SO FAR. COMBINING RESISTORS IN SERIES ELIMINATES ONE NODE FROM THE CIRCUIT. COMBINING RESISTORS IN PARALLEL ELIMINATES ONE LOOP FROM THE CIRCUIT GENERAL STRATEGY: •REDUCE COMPLEXITY UNTIL THE CIRCUIT BECOMES SIMPLE ENOUGH TO ANALYZE. •USE DATA FROM SIMPLIFIED CIRCUIT TO COMPUTE DESIRED VARIABLES IN ORIGINAL CIRCUIT - HENCE ONE MUST KEEP TRACK OF ANY RELATIONSHIP BETWEEN VARIABLES 4k || 12k 12k FIRST REDUCE IT TO A SINGLE LOOP CIRCUIT SECOND: “BACKTRACK” USING KVL, KCL OHM’S 6k I3 KCL : I1 I 2 I 3 0 Va OHM' S : I 2 6k …OTHER OPTIONS... OHM' S : Vb 3k * I 3 12 I4 I3 4 12 Vb 4k * I 4 6k || 6k KCL : I 5 I 4 I 3 0 OHM' S : VC 3k * I 5 I1 12V 12k Va 3 (12) 39 2k || 2k 1k VOLTAGE DIVIDER : VO LEARNING BY DOING 1k (3V ) 1V 1k 2k 1k 1k 2k CURRENT DIVIDER : I O 1k (3 A) 1A 1k 2k Y TRANSFORMATIONS THIS CIRCUIT HAS NO RESISTOR IN SERIES OR PARALLEL IF INSTEAD OF THIS WE COULD HAVE THIS THEN THE CIRCUIT WOULD BECOME LIKE THIS AND BE AMENABLE TO SERIES PARALLEL TRANSFORMATIONS Rab R2 || ( R1 R3 ) Y Rab Ra Rb Y Ra R1 Rb R1 R2 ( R1 R3 ) R R 1 2 R Ra Rb 3 Ra R R Ra b 3 R1 R2 R3 R1 R2 R3 Rb R2 RR R2 b 1 Rc R1 Rc REPLACE IN THE THIRD AND SOLVE FOR R1 R2 R3 R ( R R2 ) Rb Ra Rb Rb Rc Rc Ra Rb Rc 3 1 R1 R2 R3 R 1 R1 R2 R3 Rb R3 R1 Rc R R Rb Rc Rc Ra R1 R2 R3 R2 a b R1 ( R2 R3 ) Rc Rc Ra Y R1 R2 R3 R R Rb Rc Rc Ra R3 a b Ra SUBTRACT THE FIRST TWO THEN ADD TO THE THIRD TO GET Ra Y LEARNING EXAMPLE: APPLICATION OF WYE-DELTA TRANSFORMATION c R1 R3 R2 12k 6k 12k 6k 18k R1 R2 Ra R1 R2 R3 Rb R2 R3 R1 R2 R3 Rc R3 R1 R1 R2 R3 Y a b a c DELTA CONNECTION b COMPUTE IS REQ 6k 3k 9k || (2k 4k ) 10k IS 12V 1.2mA 10k ONE COULD ALSO USE A WYE - DELTA TRANSFORMATION ...