Solve this : 8 If current I3=3A sin t and I2=4A cos t, then I3 is - Physics - Alternating Current

Question

Solve this :

8   If   current   I 3 = 3 A   sin  
ωt   and   I 2 = 4 A   cos   ωt ,
  then   I 3   is   : ( 1 )   5 A  
sin   ωt + 53 °          
                 
                 
  ( 2 )   5 A   sin   ωt + 37 ° ( 3 )
  5 A   sin   ωt + 45 °    
                 
                 
        ( 4 )   5 A   sin  
ωt + 30 °

Ayushi Gupta · Accepted Answer

According to Junction Rule,
I3= I1+ I2
= 3A sin wt + 4A cos wt
= 5A (3/5 sin wt + 4/5 cos wt) [Multiplying and Dividing with
5]
= 5A (cos 53o sin wt + sin 53o cos wt) [cos
53o = 3/5 and sin 53o = 4/5]
= 5A sin (wt+53o) [sin (A+B) = sin A cos B + cos A sin
B]

Solve this : 8 . If current I 3 = 3 A sin ωt and I 2 = 4 A cos ωt , then I 3 is : ( 1 ) 5 A sin ωt + 53 ° ( 2 ) 5 A sin ωt + 37 ° ( 3 ) 5 A sin ωt + 45 ° ( 4 ) 5 A sin ωt + 30 °

Solve this :

$8 . If current I_{3} = 3 A \sin ωt and I_{2} = 4 A \cos ωt, then I_{3} is : (1) 5 A \sin (ωt + 53 °) (2) 5 A \sin (ωt + 37 °) (3) 5 A \sin (ωt + 45 °) (4) 5 A \sin (ωt + 30 °)$