How can I find Voltage V in an AC circuit using loop rules?

[MechEngrStdnt]

Homework Statement

Need to find Voltage V. I know that I need to first solve for the currents, have tried using loop rules, not having much luck.

Homework Equations

Just would like to know how to approach, and solve, this problem. ME and circuits has never been my friend, thanks!

The Attempt at a Solution

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[gneill]

You chose an excellent strategy using nodal analysis as it yields an equation in one variable that happens to be the one you want to find.

Something went wrong between your third and fourth step though, when you tried to invert the coefficient of V1 in moving it to the RHS of the equation.

 

[MechEngrStdnt]

Dealing with i has been messing me up, don't use it much in Newtonian mechanics haha. I think I'm getting further away... according to chegg the solution is 28.28<45deg. ill attach my latest attempt. Thanks for the help!

 

[gneill]

Yeah, you've done the same thing again between the final line on the left and the new line at the top right. Note:

$$\left( \frac{1}{10} + \frac{j}{10} \right)^{-1} \neq \left( 10 - 10j \right)$$

 

[MechEngrStdnt]

Wow, embarrassing...

You sir are a scholar, and gentleman. Thanks!

 

[gneill]

Glad to help!