AC Analysis Query Homework Solutions

[eeuler]

Homework Statement

I have two questions to two different problems.
The first:

The Attempt at a Solution

My attempt:

Thing is, the solutions have V2=4.986$$\angle$$111.45(degrees) and i can't seem to get to that answer at all? What is wrong with my attempt because i can't see anything wrong with it? (Unless I've left out some negative signs, but even then it shouldn't change by much? Btw i took a supernode at the two nodes, hence my long KCL eqn.)

My second question is:

Attempt:

So to find the current through the resistor, i need to firstly find the node voltages V1 and V2 right? Then it's just a simple matter of (V1-V2)/5+j15. Thing is, I'm having a difficult time trying to find V1 or V2, since as you can tell my maths gets rather messy and i just hit a wall with V1=... + V2(...). Can someone point me in the right direction? Also, i suspect that this is the 'right way' to do it, because according to the solutions, V1=6.735$$\angle$$-38.54(degrees) and V2=16.25$$\angle$$-55.52(degrees), and when i substitute in V2 into V1=...+V2(...) i get the answer of V1..so how do i actually find V1 or V2?

Thanks.

 

[KataKoniK]

I would be happy to assist you with your questions. For the first problem, it may be helpful to double check your calculations and make sure you are using the correct values for the components in your circuit. It is also possible that there may be a mistake in the solutions provided, so it may be worth double checking with a peer or your instructor to confirm the correct answer.

For the second problem, you are correct in that finding the node voltages V1 and V2 is the first step. One approach you can take is to use Kirchhoff's laws and solve a system of equations to find the values of V1 and V2. Another approach is to use a simulation software to model the circuit and find the values of V1 and V2. Additionally, if you have access to a circuit analyzer, you may be able to use that to solve the circuit and find the values of V1 and V2.

I hope this helps and good luck with your homework! If you have any further questions or need clarification, please don't hesitate to ask.