[AC Circuit] How do we convert from the time domain to the phasor domain?

[Special One]

Homework Statement

Converting

Relevant Equations

AC Circuits

In this example, We need to covert e2 & e5 to a form with imaginary number .
we will obtain e2=j10 & e5=20
Can anyone explain how we got this?

 

[berkeman]

Homework Statement:: Converting
Relevant Equations:: AC Circuits

In this example, We need to covert e2 & e5 to a form with imaginary number .
we will obtain e2=j10 & e5=20
Can anyone explain how we got this?
View attachment 262833

It looks like you can write them down by inspection of the problem statement. your are given $e_2(t)$ and $e_5(t)$ right after the "Assume" in your problem statement. Can you say what the "j" means in $e_2 = j10$?

 

[Special One]

It looks like you can write them down by inspection of the problem statement. your are given $e_2(t)$ and $e_5(t)$ right after the "Assume" in your problem statement. Can you say what the "j" means in $e_2 = j10$?

it means i. Imaginary part

 

[berkeman]

it means i. Imaginary part

LOL, yes of course. Um, let me re-phrase...

Are you familiar with the phasor representation of a sinusoidal signal?

https://www.electronics-tutorials.ws/accircuits/phasors.html

 

[berkeman]

BTW, it's hard to separate the "calculate the currents" part of the question from the "Assume" part and the part that you posted about "e2=j10 & e5=20 ".

To calculate the branch currents, I would use KCL equations to find the node voltages, but you can also use KVL equations if you prefer. But also, why would you say "e2=j10 & e5=20" when there also $\sqrt{2}$ terms in the time domain definitions?

 

[scottdave]

The $10 \sqrt{2}$ is the peak value of the sine wave. The RMS voltage for a sine wave equals $$ \frac {Vpeak } { \sqrt{2} } $$
RMS voltage is the equivalent to DC voltage. See link, below.

https://en.wikipedia.org/wiki/Root_mean_square