one week struggling to solve this electricity

[logistic_guy]

here is the question

How to find the voltage across the capacitor?



my attemp

\(\displaystyle v = iR\) this voltage across resistor

\(\displaystyle v = L\frac{di}{dt}\) this voltage across conductor

\(\displaystyle i = C\frac{dv}{dt}\) the problem for capacitor it give derivative of voltage

i need a way to get the current in term of time to be able to solve the differential equation

\(\displaystyle \int i \ dt = C\int dv\)

\(\displaystyle v = \frac{1}{C}\int i \ dt\)

i'm stuck here

 

[Perdurat]

I observed a bit of "electronic blasphemy" in your drawing:
3 passive components : a resistor, a capacitor, an inductor
3 active components: an AC voltage, an AC current, a DC
it is unusual to describe the active components like that:
i suppose you mean an AC voltage, 24Vtt (+12->-12) with a frequency of 1/3Hz and a forward faceshift of pi/2 rad with respect to the AC current, 8Att (+4->-4) with 0 rad faceshift with respect to the X-axis and a 1/2Hz frequency
that to me is a bit fouling around with Ohm's law, Kirchhoff's law, some vectors on the imagenairy plane (to simplify the equations)
or as you please:
go ballistic on the integrals and maybe discover an new "God's particle"

or do you mean 12Vtt(0->+12V) and 4Att(0->+4V)

note Vtt-> top to top as opposed to Vt-> top to 0 or Veff (1/sqrt2)

 

[khansaheb]

here is the question

How to find the voltage across the capacitor?

View attachment 38474

my attemp

\(\displaystyle v = iR\) this voltage across resistor

\(\displaystyle v = L\frac{di}{dt}\) this voltage across conductor

\(\displaystyle i = C\frac{dv}{dt}\) the problem for capacitor it give derivative of voltage

i need a way to get the current in term of time to be able to solve the differential equation

\(\displaystyle \int i \ dt = C\int dv\)

\(\displaystyle v = \frac{1}{C}\int i \ dt\)

i'm stuck here

You will NOT be able to solve this problem knowing Arithmetic only..

How many loops do see in this circuit?

 

[Perdurat]

You will NOT be able to solve this problem knowing Arithmetic only

possible but I think the problem is ill defined: symbols?,units?,rad/sec (angular velocity, Omega ) or cycles/s (frequency, Hertz ) such ill defined problem only deserves an ill defined answer:

12.45873... space wombats

 

[topsquark]

possible but I think the problem is ill defined: symbols?,units?,rad/sec (angular velocity, Omega ) or cycles/s (frequency, Hertz ) such ill defined problem only deserves an ill defined answer:

12.45873... space wombats

If it is from anywhere it would likely be a graduate Physics course or a very advanced Electrical Engineering, but as the circuit has no actual use, I doubt even that. The problem is likely made up with a number of elements randomly thrown into the circuit.

As typical with logistic_guy's style, this is likely more of a test for us than it is educational for him.

-Dan

 

[logistic_guy]

I observed a bit of "electronic blasphemy" in your drawing:
3 passive components : a resistor, a capacitor, an inductor
3 active components: an AC voltage, an AC current, a DC
it is unusual to describe the active components like that:
i suppose you mean an AC voltage, 24Vtt (+12->-12) with a frequency of 1/3Hz and a forward faceshift of pi/2 rad with respect to the AC current, 8Att (+4->-4) with 0 rad faceshift with respect to the X-axis and a 1/2Hz frequency
that to me is a bit fouling around with Ohm's law, Kirchhoff's law, some vectors on the imagenairy plane (to simplify the equations)
or as you please:
go ballistic on the integrals and maybe discover an new "God's particle"

or do you mean 12Vtt(0->+12V) and 4Att(0->+4V)

note Vtt-> top to top as opposed to Vt-> top to 0 or Veff (1/sqrt2)

thank

could you please be more organized with your notation? i'm not familiar with it.
your advise to use Ohm's law. i did. \(\displaystyle v = iR\) what's this?
the op is mixing AC and DC together which make it difficult to use Kirchhoff's law. do you have idea how to use it there?

12.45873... space wombats

is this the answer or just a guess? why not \(\displaystyle 21.45873 \ V\)

You will NOT be able to solve this problem knowing Arithmetic only..

thank

if that happen, i'll quit engineering

How many loops do see in this circuit?

3 to 4 loops

If it is from anywhere it would likely be a graduate Physics course or a very advanced Electrical Engineering, but as the circuit has no actual use, I doubt even that. The problem is likely made up with a number of elements randomly thrown into the circuit.

thank

i'm advanced engineer student. it's typical my problems are advanced too. being doubtful is good and bad, it depend on how you critirized me. if you mean i made up the op, you're wrong. if you mean the structure of the circuit don't make sense, but the author intended to make it for problem solving techniques purposes, you might be right.

As typical with logistic_guy's style, this is likely more of a test for us than it is educational for him.

-Dan

this i don't understand.

it seem you know more than the author about the problem. why not write a hint or first step to solve the problem as i was struggling for one complete week

 

[khansaheb]

3 to 4 loops

It has 3 loops - other loops would be combination of those loops.

Draw those 3 loops, along with loop currents and show us what you get.

 

[khansaheb]

Draw those 3 loops, along with loop currents

Draw those separately and indicate loop currents.

 

[logistic_guy]

It has 3 loops - other loops would be combination of those loops.

Draw those 3 loops, along with loop currents and show us what you get.

first loop \(\displaystyle I_1\)

\(\displaystyle -12\cos 3t + 6I_1 + v_0 = 0\)

second loop \(\displaystyle I_2\)

\(\displaystyle -v_0 + V_A = 0\)

third loop \(\displaystyle I_3\)

\(\displaystyle -V_A + V_{2H} + 10 = 0\)

 

[khansaheb]

Draw those separately and indicate loop currents

Where is the drawing?

 

[Perdurat]

is this the answer or just a guess? why not 21.45873 V\displaystyle 21.45873 \ V21.45873 V

no, it's called sarcasm

while the problem is stated as is, there are five problems layered on top of each other (which i am not gonna reveal)

[math]U=I*R (resistive\ load), U=I*L*\omega(inductive\ load), U=I*\frac{1}{\omega*C}\\units:R(\Omega,ohm),L(H,Henry),C(F,Farad),f(Hz,Hertz),\omega(rad/s)[/math]
understanding the consept of a static vector (ohm law with respect to resistive load:U,R,I can be represented as static vectors on the X-axis)
expanding on the idea: resistive networks (algebra:serie,parallel,compound,2D,3D,....)

understanding the concept of a rotating vector (goniometry:the unit circle,pythagoras,thales,...)
[math]f(x)=sin(x)\\the\;zero's(0): \sum_{n=0}^{\infty}n*\pi\\the\; maxima(+1) : \sum_{n=0}^{\infty}n*\frac{\pi}{2}\\the\;minima(-1):\sum_{n=0}^{\infty}n*\frac{3\pi}{2}[/math]
the basic idea: a vector rotating counterclockwise) around a centerpoint (0,0)
[math]the \;amplitude \; of \;the \;sine : f(x)= a*sin(x),x\in \R\\ the\; phase\; of\; the\; sine : f(x)=sin(x+\alpha),\alpha\; in\;rad\\ the\; frequency\; of\; the\; sine : f(x)=sin(x*n), n\in\N\\[/math]
understanding the consept of a rotating angle (2 rotating vectors locked in phase):
[math]resistor:\alpha=0,\overrightarrow{\rm U}=\overrightarrow{\rm I}\\ capacitor:\alpha= \pi,\overrightarrow{\rm U}+\pi=\overrightarrow{\rm I}\\ inductor:\alpha= \pi, \overrightarrow{\rm U}-\pi=\overrightarrow{\rm I}\\[/math]
understanding a compound power source as: an offset vector (DC component), which displaces the centerpoint of the rotating vector or rotating angle from (0,0) to ...
expanding on the idea: imaginairy plane, fourier transform, hartley transform, digital signal processing, ....

last but not least: finding the angle where the capacitor changes from charging to discharging and the for the inductor: where
the magnetic flux is changing from building up to inducing a current (or @ which angles the current changes direction)
once you determine those angles THEN you write the integral equation (and solve your problem)

 

[Perdurat]

theamplitudeofthesine:f(x)=a∗sin(x),x∈R

correction:

a∈R

 

[mario99]

I studied AC circuits analysis when I was a student. I had to dig deep in the last few hours to remember the rules. This electric circuit can be solved by a method called phasors. It is somehow similar to what @Perdurat has written, but I will explain it in an everyday used notation and in a more educated style.

A phasor is just the amplitude and the phase shift of a sine wave written in a complex style. ([imath]z = x + jy[/imath])

This method of phasors basically transforms the time domain to the frequency domain. The question remains why not working in the time domain directly?! Because the time domain depends on initial conditions. When these conditions are absent like post #1, our friend the frequency domain is the best choice because he does not care about the initial conditions.

This complex style above was written in rectangular form. It can also be written in polar and exponential forms, [imath]\displaystyle z = r\angle\phi[/imath], [imath]\displaystyle z = re^{j\phi}[/imath], respectively.

All the forms above can be written as [imath]\displaystyle z = r(\cos \phi + j\sin\phi)[/imath], where [imath]\displaystyle r = \sqrt{x^2 + y^2}[/imath] and [imath]\displaystyle \phi = \tan^{-1}\frac{y}{x}[/imath].

The first step is to convert the formulas in post #1 from the time domain to the frequency domain.

Time Domain [imath]\ \ \ \ [/imath] Frequency Domain

[imath]\displaystyle v = iR \ \ \ \ \ \ \ \ \rightarrow \ \ \ \ \ V = IR[/imath]

[imath]\displaystyle v = L\frac{di}{dt} \ \ \ \ \ \rightarrow \ \ \ \ \ V = j\omega LI[/imath]

[imath]\displaystyle i = C\frac{dv}{dt} \ \ \ \ \ \rightarrow \ \ \ \ \ V = \frac{I}{j\omega C}[/imath]

The second step is to convert the components in the circuit from the time domain to the frequency domain.

[imath]\displaystyle 6 \ \Omega \ \ \ \ \ \rightarrow \ \ \ \ \ 6 \ \Omega [/imath]

[imath]\displaystyle 2 \ \text{H} \ \ \ \ \ \rightarrow \ \ \ \ \ 2j\omega \ \Omega [/imath]

[imath]\displaystyle \frac{1}{12} \ \text{F} \ \ \ \ \ \rightarrow \ \ \ \ \ \frac{12}{j\omega} \ \Omega [/imath]

[imath]\displaystyle 10 \ \text{V} \ \ \ \ \ \rightarrow \ \ \ \ \ 10 \ \text{V} [/imath]

[imath]\displaystyle 12\cos 3t \ \text{V} \ \ \ \ \ \rightarrow \ \ \ \ \ 12\angle 0^{\circ} \ \text{V}[/imath]

[imath]\displaystyle 4\sin 2t \ \text{A} \ \ \ \ \ \rightarrow \ \ \ \ \ 4\angle 0^{\circ} \ \text{A} [/imath]

The third step which is the most important one is to choose the method of analyzing. For example, professor Khan has chosen to use three loops. I have a different analyzing method in mind, but I will wait for the OP to confirm that he understood what I have written.

 

[Perdurat]

If it is from anywhere it would likely be a graduate Physics course or a very advanced Electrical Engineering, but as the circuit has no actual use, I doubt even that. The problem is likely made up with a number of elements randomly thrown into the circuit.

As typical with logistic_guy's style, this is likely more of a test for us than it is educational for him.

-Dan

it could be something like: I been strugling for a week... (every time I picked up this problem, given a week time from the teacher/professor to work on it at home, i found out that it gave me great stress releave to push the button of my X-box, however as a tested the method over and over again and the method proved to be valid, with one day left i pushed the X-box button again, however this time I experienced a certain kind of numbness of the brain...odd.....HELP!!!!!!

 

[blamocur]

I studied AC circuits analysis when I was a student. I had to dig deep in the last few hours to remember the rules. This electric circuit can be solved by a method called phasors. It is somehow similar to what @Perdurat has written, but I will explain it in an everyday used notation and in a more educated style.

I don't have any experience in this area, only questions According to Wikipedia: "A common application is in the steady-state analysis of an electrical network powered by time varying current where all signals are assumed to be sinusoidal with a common frequency." But in the op there are two sources (voltage and current) with different frequencies -- would you still expect phasors to be useful there?

 

[Perdurat]

but I will explain it in an everyday used notation and in a more educated style.

time domain X-axis->time, Y-axis->amplitude
frequency domain: X-axis->frequency, Y-axis->amplitude
euclidean plane: X-axis->scalar, Y-axis->scalar
imaginairy plane: X-axis->scalar, Y-axis->j*scalar

[math]12cos3t\; V->12cos6\pi\;V*rad*s^{-1} = 12sin(\frac{11}2\pi)\;V*rad*s^{-1}\\ 4sin2t\; A->4sin4\pi\;A*rad*s^{-1}[/math]
(i think, ill defined...)

6 Ω → 6 Ω

2 H → 2jω Ω\displaystyle 2 \ \text{H} \ \ \ \ \ \rightarrow \ \ \ \ \ 2j\omega \ \Omega 2 H → 2jω Ω

112 F → 12jω Ω\displaystyle \frac{1}{12} \ \text{F} \ \ \ \ \ \rightarrow \ \ \ \ \ \frac{12}{j\omega} \ \Omega 121 F → jω12 Ω

(again):
resistive load: current is in fase with voltage
capacitive load: voltage lagging behind current by 90° (pi/2)
inductive load: current lagging behind voltage by 90° (pi/2)
if you want to incorporate the resistance (1x), capacitance (2x), inductance (2x) in the vector diagram, then express them as their values multiplied with their resp current, otherwise take you're phasor and get yourselve a role in the Harry Potter franchise

 

[mario99]

I don't have any experience in this area, only questions According to Wikipedia: "A common application is in the steady-state analysis of an electrical network powered by time varying current where all signals are assumed to be sinusoidal with a common frequency." But in the op there are two sources (voltage and current) with different frequencies -- would you still expect phasors to be useful there?

Yes, I would. And I think that it is the only way to attack this problem. (Ignoring simulations and similar stuff.)

(i think, ill defined...)

Are you trying to say that the circuit problem is not well defined, so it cannot be solved?

Well .... do you think that guy, I don't remember his name, who solved the Airy equation from scratch last year, a simple electric circuit would stop him now?

Note: Give a man a fish and you feed him for a day. Teach a man to fish and you feed him for a lifetime.

 

[Perdurat]

Are you trying to say that the circuit problem is not well defined, so it cannot be solved?

"the world of math" is huge. it is reasonable to state that it expanded on the idea of counting (sheep), it is also reasonable that one learns to add, multiply,divide,...before (university) or before specialising in a branch (profession).
if one has a piece of land and one keeps chickens to feed himselve and his family, one can balance between investing in the fence (not to feed the fox) or aquire a rooster (have more chickens)...However if one feeds the chickens and the rooster, one might observe that a chicken rather flies the fence than to be subject to nature's call (and hence feeds the fox). A pragmatic solution for that problem could be: clipping one wing of the chicken(s).
in that respect (ohm's law):
a clipped chicken: U=I*R, P=I*U
a balanced chicken: P=I^2*R

there is a reason for "clipping" the problem (let go of the sheep), there could be a reason for observing that the problem is ill defined:

observing the drawing:
-you can not separate the power sources from the passive components therefore, the power sources are ill defined:
try to connect one wire of an AC power source (lets take the AC current source) and connect to the DC power supply (common)
the other wire connect both power sources via a 1ohm resistor, now "get some extra batteries" (10V-100V-1000V)
"quite"an intresting current source, no?

off coarse the problem can be solved:
there are 2 "frequencies" defined so you convert the problem first to a CORRECT vector diagram. Because a product of a qualifier and a quantifier is a point (the passive components), they have no meaning nor in the time domain, nor in the frequency domain

then you observe the "ill" defenition (2t,3t), which are suggestions of a time domain but also a defenition of a product of a time unit (1sec) and the first 2 primes... therefore: "the balanced chickens": (subharmonics,1/x, harmonics) (2:1/2n,1,2n),(3:1/3n,1,3n)
then you double check if your vector diagram is CORRECT upon which you define the filtermask
then you convert the 2 AC signals

 

[Perdurat]

then you convert the 2 AC signals

then you convert the 2 AC signals from the time domain to the frequency domain
then you apply your filtermask and convert back to the time domain...

note:
did you know that the "inventor" of the von neumann architecture struggled to find a business case for "his" invention?
(if that man had access only to 2 X-box on-off switches and 2 indicator lights (smiley,thumbs up) where would we be now?

did you know that the black knights on a chess board are based upon a knight who had to much beans for breakfast,
while the white nights are based upon a knight who observed that a horse, carrying a full armored knight could not jump a farmer?

q: what is the airy equation about?

 

[Perdurat]

q: what is the airy equation about?

never mind, i looked it up (differential equations, never granted education on that topic)