AC Circuit Analysis (Nodal RMS)

[planauts]

Homework Statement

The question is:

The given answer is:

Homework Equations

The Attempt at a Solution

I already got the "correct" answers.

My question is, I used Vrms voltage and Irms current to solve the nodal analysis. Would it be incorrect to use Vpeak and Ipeam to solve the circuit. Would it yield a similar result? I mean, would I be able to divide Va(peak) by sqrt(2) and get Va(rms)?

I understand that the author's intent was to use Vrms and Irms since the second part of the question requires to calculate Power, which is usually done using RMS values to avoid dividing by 2.

 

[gneill]

Sure, you can use peak or average or any other scaled version of the voltages and currents so long as you "revert" to rms when required (such as determining average power). This works so long as all the sources are sinusoidal and the circuit is linear.

 

[rude man]

Yes, V =√2V_rms for all your voltages so either way you'd get the right answers.

In general, the phasor for V₀sin(ωt + θ) is [V₀/√2]e^jθ.

 

[planauts]

The reason why I asked this question was when I originally did the question with V_max, it did not match the given answers (even after dividing by sqrt(2) to the given rms). I knew it did not make since I was just multiplying all the currents by a factor. When I did the question again using V_max, it turned out that I had originally made a mistake some where. Math makes sense and the universe is in order!
The algebra gets tedious when solving systems of linear equation with complex values.

Thank you both for the confirmation.