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

AI Thread Summary
To convert from the time domain to the phasor domain in AC circuits, the voltages e2 and e5 can be expressed as e2 = j10 and e5 = 20, where "j" represents the imaginary unit. This conversion typically involves recognizing the peak values of sinusoidal signals and applying the RMS formula, which states that RMS voltage equals the peak voltage divided by the square root of 2. The discussion highlights the importance of understanding phasor representation and the relationship between time domain definitions and their corresponding phasor forms. Additionally, using Kirchhoff's Current Law (KCL) or Kirchhoff's Voltage Law (KVL) can help calculate branch currents in the circuit. Understanding these concepts is crucial for accurately analyzing AC circuits.
Special One
Messages
32
Reaction score
1
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?
Screenshot 2020-05-15 at 22.55.53.png
 
Physics news on Phys.org
Special One said:
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##?
 
berkeman said:
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
 
Special One said:
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

1589585090600.png
 
  • Like
Likes scottdave and DaveE
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?
 
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
 
  • Like
Likes berkeman
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Back
Top