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3-Assignment3_Solution

3-Assignment3_Solution - ELECTRICAL ENGINEERING DEPARTMENT...

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ELECTRICAL ENGINEERING DEPARTMENT CALIFORNIA POLYTECHNIC STATE UNIVERSITY EE 255 Assignment #3 Problem 1: The magnetic core shown in the figure has the following parameters: . 60 , 5000 turns, 1000 N , cm 25 A , cm 10 r 2 c Hz andf l c = = = = = μ For a current of A ) cos( 5 ) ( t t i ϖ = , determine: (a) Flux in the core, (b) Flux linkage, (c) Inductance, and (d) Induced voltage. ) ( t i N - + ) ( t e Solution: a) Flux: wb t KA A l C / . * . * * * * - = = = - - - 37 6 10 5 2 10 4 5000 10 10 R 4 7 2 C π μ wb t t R t Ni t C C ) cos( . * . ) cos( * ) ( ) ( ϖ ϖ ϕ 785 0 10 37 6 5 1000 3 = = = b) Flux linkage: t wb t t t N t C - = = = ) cos( ) cos( . * ) ( ) ( ϖ ϖ ϕ λ 785 785 0 1000 c) Inductance: H 157 5 785 = = = ) cos( ) cos( ) ( ) ( t t t i t L ϖ ϖ λ d) Induced voltage: V 785 ) sin( ) ( ) ( t dt t d t e ϖ ϖ λ - = = rad/s 377 60 2 2 = = = * π π ϖ f KV 90 296 377 785 ) cos( ) sin( * ) ( ° + = - = t t t e ϖ ϖ KV 90 296 ° = rms E
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Problem 2: A 3 KVA, 480:240-V, 60-Hz single-phase ideal transformer is supplying a load impedance of 15 + j20 at 240 V. Determine the load current, source current and the impedance seen by the source. 1 I - + V 480 - + V 240 L I I = 2 + 20 15 j A 53.13 - 9.6 13 53 25 0 240 20 15 0 240 ° = ° ° = + ° = . j I L A 53.13 - 4.8 480 240 53.13 - 9.6 ° = ° = * Source I + = ° = ° = 80 60 53.13 100 240 480 53.13 25 2 j Z L ) ( * P roblem 3:
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