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 When I did the question again using V_max, it turned out that I had originally made a mistake some where.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.

 

[rezeew]

However, in theory, using Vpeak and Ipeak should also yield the same results as long as the peak values are converted to RMS values before calculating power.

In general, it is not incorrect to use Vpeak and Ipeak to solve a circuit using nodal analysis. However, it is important to note that converting peak values to RMS values before calculating power is necessary to ensure accurate results. This is because power is proportional to the square of the voltage or current, and using peak values would result in a different value compared to using RMS values.

Using Vpeak and Ipeak to solve a circuit may also be more time-consuming and complex compared to using Vrms and Irms. Therefore, it is recommended to use Vrms and Irms when solving AC circuits using nodal analysis.

In conclusion, while using Vpeak and Ipeak may yield similar results to using Vrms and Irms in nodal analysis, it is important to convert peak values to RMS values before calculating power to ensure accuracy. It is also more efficient to use Vrms and Irms in nodal analysis.