ProblemSet1_Solution

# ProblemSet1_Solution - Problem Set#1 Basic concepts complex...

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1 Problem Set #1 Basic concepts – complex algebra and three-phase balanced circuits 1-1 (Grainger and Stevenson, Jr. Chapter 1, Prob 1.12) Evaluate the following expressions in polar form: Solution: a) a -1 = 1.732 150 ° b) 1- a 2 + a = 2.00 60 ° c) a 2 + a +j = 1.414 135 ° d) ja + a 2 = 1.932 225 ° 1-2 (Grainger and Stevenson, Jr. Chapter 1, Prob 1.13) Three identical impedances of 10 -15 ° are Y-connected to balanced three-phase line voltages of 208 V. Specify all the line and phase voltages and the currents as phasors in polar form with V ca as reference for a phase sequence of abc . Solution: Since V ca =208 0 ° V, V an =120 210 ° V, V bn =120 90 ° V, V cn =120 -30 ° V. Therefore, A 225 12 ° = = Z V I an a , A 105 12 ° = = Z V I bn b , A 15 12 ° = = Z V I cn c 1-3 (Grainger and Stevenson, Jr. Chapter 1, Prob 1.14) In a balanced three-phase system the Y-connected impedances are 10 30 ° . If V bc =416 90 ° V, specify I cn in polar form.

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ProblemSet1_Solution - Problem Set#1 Basic concepts complex...

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