# Solution HW1 - ECE 430 HW #1 Solution 2.1) 100 v(t ) = 100...

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ECE 430 HW #1 – Solution 2.1) 100 ( ) 100cos(377 10 ) 2 cos(377 10 ) 2 vt t t ⎛⎞ =+ ° = ⎜⎟ ⎝⎠ + ° V 100 10 2 V ⇒= ° V 1 ( ) cos(377 55 ) 2 cos(377 55 ) 2 it t t ° = + ° A 1 55 2 I ° A Average power: 100 1 50 cos( ) cos(10 55 ) 22 2 vi PV I W θθ =− = ° ° = power factor: 1 cos( ) cos(10 55 ) 2 PF ° = leading 2.2) (a) 100 ( ) 100cos(377 15 ) 2 cos(377 15 ) 2 t t ° = + ° V 100 15 2 V ° V 10 ( ) 10sin(377 45 ) 2 cos(377 135 ) 2 t t + ° = + ° A 10 135 2 I ° A Average power: 100 10 cos( ) cos(15 135 ) 250 I W = ° ° = (b) 100 ( ) 100cos(377 75 ) 2 cos(377 75 ) 2 t t ° = ° V 100 75 2 V ° V 10 ( ) 10sin(377 15 ) 2 cos(377 105 ) 2 t t + ° = + ° A 10 105 2 I ° A Average power: 100 10 cos( ) cos( 75 105 ) 500 I W = ° ° = (c) () ( ) ( ) 2 100 sin(377 30 ) 2 100 cos(377 120 ) t t ° = − ° V 100 120 V ⇒=∠ −° V ( ) 2 10 cos(377 60 ) t ° A 10 60 I A Average power: ( )( ) ( ) cos( ) 100 10 cos( 120 60 ) 500 I W = ° ° = power factor: ( ) cos( ) cos( 120 60 ) 0.5 PF = ° ° = leading (d) 100 ( ) 100sin(377 30 ) 2 cos(377 60 ) 2 t t ° = ° V 100 60 2 V ° V 10 ( ) 10sin(377 120 ) 2 cos(377 30 ) 2 t t ° = + ° A 10 30 2 I ° A

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Average power: 100 10 cos( ) cos( 60 30 ) 0 22 vi PV I W θθ ⎛⎞ =− = ° ° = ⎜⎟ ⎝⎠ power factor: cos( ) cos( 60 30 ) 0 PF θ = ° ° = leading (since iv > ) (e) 10 10 10 2 45 Vj =+ = ∠° V 5 10 5 5 63.43 Ij = ° A
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## This note was uploaded on 02/21/2010 for the course ECE 430 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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Solution HW1 - ECE 430 HW #1 Solution 2.1) 100 v(t ) = 100...

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