Question

IF=1.5IL, IL=200, IP=(?)​

Answer 1

Answer:

Ip1=Ip, direction 0°,

Ip2=Ip, direction -120°

So if you write them like complex numbers, it looks like:

Ip1=Ip,

Ip2=-1/2 Ip - Root(3) / 2 Ip i

Next step is IL=Ip1-Ip2:

IL=Ip + 1/2 Ip + Root(3) / 2 Ip i,

IL=3/2 Ip + Root(3)/2 Ip i.

Now get back in polar form:

IL=Root( (3/2* Ip)2+(Root(3)/2* Ip)2)

IL=Root(3*Ip2) = Root(3) * Ip

Direction of line current is: 

arctan =Im(IL) / Re(IL),

so:

arctan=(Root(3)/2)/(3/2) = 30°.