6 . Two alternating current electrical sources are given as V1 �23sin ( 6� t�
0.17 )
6�ti and V2 �Im ( e ( z � w)) respectively , where t represents time in seconds , and z , w� . The total voltage V is given by V �V1� V2 � 29sin ( 6� t � 0.31 ) .
( a ) Find the expression of z� w, where z is in the form
( b ) Express the following in the form r( cos� � isin �)
:
0.31i re � . [ 3 ]
( i ) z
( ii ) w
( c ) It is given that i z �w � Le � . Find
[ 2 ]
( i ) L ;
( ii ) � .
( d ) Hence , express V
2 in the form Asin ( Bt � C) , A , B , C � .
[ 6 ]
[ 3 ]
© SE Production Limited 22 All Rights Reserved 2021