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exam3

# exam3 - EE321 Exam 3 Spring 2006 Handy Identities sin A B =...

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EE321 Exam 3 Spring 2006 Handy Identities: 2 / 1 ) 3 / 2 cos( 2 / 3 ) 3 / 2 sin( = = π π 7 0 10 4 = π µ H/m Important Note: Since calculators are not allowed, you can have π in your answer to any problem. ( ) ( ) ( ) dx du u u dx d dx du u u dx d B A B A B A B A B A B A B A B A B A B A B A B A B A B A B A cos ) sin( sin ) cos( ) sin( ) sin( 2 1 cos sin ) cos( ) cos( 2 1 sin sin ) cos( ) cos( 2 1 cos cos sin sin cos cos ) cos( sin cos cos sin ) sin( = = + + = + = + + = = ± ± = ±

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1.) 8 pts. Physically speaking, what does the winding function tell us? 2.) 15 pts. Consider a machine with the winding pattern below. How many poles does the machine have ? Find the discrete winding function. T as N ] 5 5 5 5 5 5 5 5 5 5 5 5 [ = 3.) 15 pts. The conductor density (positive out) of a machine is given by ) 12 cos( 50 ) 4 cos( 100 sm sm as n φ φ = How many poles does the machine have? Compute the winding function. 4.) 7 pts. What is the effect of the number of poles on the speed of the machine? 5.) 15 pts. The winding functions of the a- and b- phase of a machine are given by ) 4 sin( 10 ) 4 cos( 10 sm bs sm as w w φ φ = = The machine currents are given by ) 30 sin( 5 ) 30 cos( 5 t i t i bs as = = Find the speed and direction of the stator MMF.
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