Here is my solution (first I found out the resistances of the capacitors/inductors with omega as 50, then found the total current in the circuit, and then Va by summing up the voltages from the + terminal to the -ve terminal):

KVL,

60<20 + I(2 - 2j + 2.5j + 4j + 5 + 5j) + 100<0 = 0
Calculator gives I as 13.37<-46.14

Va = I(-2j + 2.5j + 4j + 5) + 100<0
Va = (13.37 < 46.14) (7 + 4.5j) + 100<0
Va = 163.31 < 41.94...

What exactly have I done wrong and what would be a good way to solve this question? Also tried a bunch of different things, always get some wrong answer.

 

First, you want to start using terminology correctly -- you aren't finding the resistances, but rather the reactances.

Second, you want to start using units properly. The frequency isn't 50, it is 50 rad/sec. Similarly, 60<20 is not a voltage, it's not even a properly dimensions phasor since the angle is not specified as being in either degrees or radians (and the default is radians!). It should be 60V<20° (some people write it as 60<20° V, which if fine). So your equation (including the errors in it) should have been expressed as:

60V<20° + I(2Ω - 2jΩ + 2.5jΩ + 4jΩ + 5Ω + 5jΩ) + 100V<0° = 0

If you can't represent the degree symbol use 'deg' and if you can't represent the ohm symbol use 'ohm'.

Third, THANK YOU for showing your attempt at a solution!

Fourth, you have "I" in your KVL equation but you never define it. More specifically, you don't indicate if it is the current going clockwise or the current going counterclockwise. Don't make people, particularly the grader, have to guess. In this case, we can't even make a good guess because the equation you provided is not consistent with either. This makes for more difficult communication because we can't be sure we are on the same page.

Fifth, you need to decide if you are summing up the voltage gains or the voltage drops as you go around the loop. You are mixing the two and that is your basic problem.

Sixth, learn to do sanity checks. For instance, shouldn't the impedances on all of the capacitors have the same sign in your KVL equation? Likewise for the inductances? And do the relative signs on the two sources make sense?

Try to apply those thoughts