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# 41 Class Note for ECE 20100 with Professor Tan at Purdue

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This 7 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Purdue University taught by a professor in Fall. Since its upload, it has received 18 views.

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Date Created: 02/06/15
ECE201 Linear Circuit Analysis I Prof H Z Tan Topic InductorCapacitor Combinations Duality 1 Inductor Combinations 1 Principles 1 Inductors in series add to form Leq LeqL1 LZ Ln 2 For n inductors in parallel Reciprocal of sum of reciprocals law Derivation of Principle 1 iin1 vi g LI Vina 7 v E L2 L V3 E 3 di t Vin t D Leq 1 Vin t V1 V2 V3 kVL in di di L J L dt 2 3 dt dt L1L2L3di quot1 Ll Leq Derivation of Principle 2 H3 39 t 0 I 2 lin Vin t g E L1 L2 Leq di t di v V t D L 1 gtl i l Sq Leq di t di v t L 11 Vln 1 dt dt L1 di t di v VinlttgtL2 Zf d ff 2 di t di v EBTH ii i1i2 i3 kCL diint di1t dim also dt dt dt dt Vig rirh Leq L1 L2 L3 1 1 1 1 Leq L1 L2 L3 Remark Inductor combinations satisfy the same formula as resistors 2 Voltage division formula n di v1 L1 1 di inLeq if L1 V V1 vi Leq L1L2L3 General V k L k n total ofL s Vin E Li i1 3 Current Division Formula ik k General n n total of parallel 1nductors 1in K 1 Z i1 L1 Derivation 0 U1 U2 1i3 1m t Vin t g g g L1 L2 L3 Leq 1L11LZ 1L3391 1 39t 110 L Vin TNT 1 co 1 l 1int J Vin TNT Leq 7w 7L1 iint74eq 2 Capacitor Combinations 1 Principles 3 For n capacitors in series 4 Capacitors in parallel add Ceq C1C2Cn Derivation of Principle 3 iin V1 Cl mm D V2 C2 gt V3 7 c3 By de nition ii D Ceq 13 vi v1 v2 v3 kVL dvc dvc i From icCF FE Derivation of Principle 4 111 liz 1i3 139 v 1n 1n C1 C2 C3 Ceq dvin Be de nition ii D C sq dt ii i1i2 i3 kCL C1 dvin C2 dvin C3 dvin dt dt dt dv C C C 1 2 3 dt Ceq 2 Voltage Division Formula series circuit Vin n K 1 j Z i1 C1 3 Current Division Formula Ck ik 1in M Ci 1 11 total of capacitors in series 11 total of capacitors in parallel 3 Examples 1 Find Leq and 10m 2 Find Ceq and vent i 8mF 12ml 0 18mmquot 24mF 60an vom O 7

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