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EE_387_200809FA_homework_01

# EE_387_200809FA_homework_01 - EE 387 Homework 01 Fall 2008...

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EE 387 Homework 01 Fall 2008 Due on Thur. Sept. 4 at the EE Homework Slot outside of 121 EE East before 4:30 p.m. 1. Simplify the following matrix-vector product to the shortest possible expression: + 1 ( ) 2 120cos( ) V vt t ω =⋅ 1 () 0.5 Ω 2.5 mH 2 20 Ω 40 mH 50 F μ + it cos( ) cos( ) sin( ) sin( ) sin( ) cos( ) e e t tt t ϕ ωω + ⎡⎤ ⎢⎥ + ⎣⎦ 2. The network shown to the right is operating in the sinusoidal steady state with 26 0 r a d / s π . a. Determine the value of I ± . b. Determine the value of V 2 ± c. Express . d. Express . 2 For problems 3 and 4 consider a single-phase load for which the voltage and current are expressed: ( ) 2 240cos( 15 ) V t =+ ° 218cos ( 15)A t =− ° where 0 r a d / s . 3. Power calculations: a. Determine the apparent power and power factor. b. Determine the real and reactive power. c. Sketch the power triangle. 4. Phasor diagram: a. Sketch a phasor diagram. Assume that the voltage scale is 10 times that of the current scale. b. Express the components of i ( t ) that are in phase and in quadrature with the voltage, i p ( t ) and i q ( t ).

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EE_387_200809FA_homework_01 - EE 387 Homework 01 Fall 2008...

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