Applying Thevenin's theorem to AC circuits

[mpar3]

Homework Statement

FIGURE 1 shows a 50 Ω load being fed from two voltage sources via
their associated reactances. Determine the current i flowing in the load by:

(a) applying Thévenin’s theorem
(b) applying the superposition theorem

Relevant Equations

Thevenin equivalents, polar & rectangular conversions

So I've seen other threads on here with the same problem from a few years ago, and I'm just not getting the same answers. However, I followed along with a similar problem in the textbook and used all the same methods, so can't understand where I've gone wrong, or if I even am wrong. Also not sure if its ok that the current should be at an angle greater than 90 degrees

 

[The Electrician]

See the first few posts in this thread: https://www.physicsforums.com/threads/thevenins-theorem.775385/

You have the sign of the imaginary part of the 50 Ω load wrong.

 

[mpar3]

See the first few posts in this thread: https://www.physicsforums.com/threads/thevenins-theorem.775385/

You have the sign of the imaginary part of the 50 Ω load wrong.

I thought a lagging power factor leads to a negative phase angle, and thus a negative imaginary component. Is that not right?

 

[The Electrician]

I thought a lagging power factor leads to a negative phase angle, and thus a negative imaginary component. Is that not right?

That is not right.
Look here: https://en.wikipedia.org/wiki/Power_factor#Lagging_and_leading_power_factors

Part way down the page under the heading "Lagging and leading power factors" you'll find discussion of the topic.

 

[mpar3]

That is not right.
Look here: https://en.wikipedia.org/wiki/Power_factor#Lagging_and_leading_power_factors

Part way down the page under the heading "Lagging and leading power factors" you'll find discussion of the topic.

I don't know why I was so set on it being negative. I think I must have mixed it up with the angle between current and voltage maybe. Thanks for your help