For anyone reading this in the future: I've figured it out.
The unit vector ##\hat{a}_{\rho}## does not mean: ##\rho=1##, ##\phi=0##, ##z=0##. ##\hat{a}_{\rho}## actually depends on ##\phi## as it's ##\left( cos\phi,sin\phi,0 \right)##.
So to simplify things, would I be correct in saying that ##{ { \hat { a } } }_{ ρ }## depends on ##\varphi## because the cylindrical coordinate system has ##\varphi## as one of its components but ##{ { \hat { a } } }_{ x }## does not depend on ##\varphi## because the rectangular coordinate...
Alright, thank you for mentioning that vector integrals work like scalar integrals.
You said earlier that "If you use curvilinear coordinates, the basis used depends on the point in space." I'm not sure what you're referring to when you say "the point in space" since the integral in the...
It seems this is going over my head. Do you know what I can read to understand vector integrals?
I already completely Calculus 3, and I did double integrals, triple integrals, line integrals, surface integrals, green's theorem, stoke's theorem, divergence theorem, etc. But I don't recall ever...
Sorry, I'm having trouble understanding. I'm a little rusty on linear algebra. The basis is "vectors that are linearly independent and every vector in the vector space is a linear combination of this set". But you can only take the basis of a vector space. Are you saying I should take the basis...
Question:
Solution:
The notation used is: ##(x,y,z)## is for rectangular coordinates, ##(\rho,\varphi,z)## for cylindrical coordinates and ##(r,\theta,\varphi)## for spherical coordinates. ##{ { \hat { a } } }_{ ρ }## represents the unit vector for ##\rho## (same applies to ##x, y, z##...
It seems to me that both PN junctions and transistors act as switches. And both switches are voltage-controlled. So what advantage does a transistor have over a PN junction? When the voltage is high on a PN junction, it is in forward bias and it allows current to pass though. When the voltage is...
Is there any reason why logic gates are built using transistors instead of PN junctions? Wouldn't it be more cost-efficient to use PN junctions? I am referring to CMOS logic gates.
Also, what can a transistor do that a PN junction can't?
Do LUTs need to look exactly like this below? Or can LUTs be any sort of box that has 2 inputs and 1 output?
Also, do LUTs need those pink squares? i.e. stored 1's and 0's inside the LUT as memory.
Homework Statement
Homework Equations
The Attempt at a Solution
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The multiplexer that is closest to the top of the page has ~x3 as an input but I am not allowed to use the negation of a logical variable as an input. Any way to get rid of this negation?
Homework Statement
Homework Equations
The Attempt at a Solution
Here is my solution:
Is this the most efficient solution? I have to minimize the number of multiplexers I use so I think this is optimal, correct?[/B]
Homework Statement
Homework Equations
The Attempt at a Solution
[/B]
Is there any more efficient way to solve this problem? The resultant functions are quite complicated and I was wondering if there is any way to make them simpler so it would be easier to draw the circuit.
Homework Statement
Homework Equations
The Attempt at a Solution
I am unsure how to proceed from here. Here is what I understand LUTs to look like:
Here is my attempt so far:
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I just did it this way and it seems to be correct. Is there anything I did wrong with my method?
Actually, I think I figured out what I did wrong. I substituted C=0.25 instead of C=1 and I substituted L=1 instead of L=0.25. Opps.
The problem is that the provided solution doesn't derive the differential equations from scratch. It uses equations that we are supposed to memorize. I would prefer to just solve the problem from scratch instead of plugging in and chugging. I am trying to derive the differential equations from...
Homework Statement
Homework Equations
Here is the technique I am using:
The Attempt at a Solution
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I understand how to solve the problem using the technique provided by the solution but I was wondering where I messed up in the technique that I used. I prefer the second...
From Wikipedia, the following diagram explains the energy emitted when an electron jumps from a higher-energy shell to a lower-energy shell:
I already know that the energy of a single photon is equal to ##hf## and in this diagram, ##\Delta E=hf##. Does that mean that ##\Delta E## is only one...
So my textbook is explaining the hall effect and the following equation was derived:
∆VH=vd·B·W
But if you look at the diagram, it appears that vd is pointing both ways. So which direction is vd pointing in? Or is this because electrons in the opposite direction is the same thing as holes in...
Thank you for this. Argh, I wish my textbook explained this to me. Why does the inductor and capacitor act as closed/open circuits in the steady state but not in the transient phase?
You could try bookmarking: https://www.physicsforums.com/watched/threads/all but there really should be a way to access this link directly from the Forums menu.
I think I figured it out. At ##t=0^-##, the capacitors are replaced with open circuits and the inductors are replaced with wires but this does not apply at ##t=0^+##.
Problem:
Attempt:
But here is what happens when I apply nodal analysis to the same node at t>0:
Is this a contradiction? Is the voltage of the resistor at t=0+ equal to 16V or 0V?
I understand that negative resistance is impossible in the real world, but shouldn't I at least get an answer with negative resistances in the math? I didn't even get an answer in the algebra which is confusing me.
Is there any specific reason why you can't the following equation to:
to:
vo=3v1-2v2?
I understand that I get 0=0 but why do I get 0=0? Algebraically speaking, why would it matter if it were vo = 3v2 - 2v1 or vo=3v1-2v2?
Sure, here is the drawing of the general circuit that I am aiming to design:
For that general circuit, the following equation applies:
Here is an example in the textbook:
Homework Statement
Homework Equations
The Attempt at a Solution
Here is my attempt: http://i.imgur.com/oKjwI8O.png
The problem is at the end, I get 0=0. What did I do wrong?
Why so?
Is it because the circuit is open when it is disconnected? My model actually uses inductive charging so as far as I know, the circuit is always closed.
I have two questions.
1. A lot of voltage dividers are wired up like this:
Is there any reason why they can't be wired up like below?
2. When should a voltage regulator be used instead of a voltage divider?
The external power supply is just a wall wart. The only way I can see that I will be harmed is if water somehow ends up near the electric socket. You take the same risk with any battery-powered toothbrush anyway because you need the charger connected to an electric socket.
Anyways, it looks...
Does a dead 1.2V rechargeable AA NiCad battery act as an open or closed circuit?
My electric toothbrush's rechargeable battery recently died and the manufacturer expects me to replace the entire unit. Personally, I think that's a waste of money so I've already opened it up and I can see the...
For anyone reading this in the future, this is how I would now solve this problem.
First, draw a diagram:
With basic series addition:
And now we can draw this diagram to solve for V (labelled Vx in the diagram):
Ah, that clarifies a lot and I feel like I finally understand it. Of course, in a RL Parallel circuit, the voltages would all be the same (with the same phase angle) and the phase angles would be different in the current because the impedance must be completely resistive for resistors and...
How do you know that the inductor's voltage is completely imaginary/reactive? Is it because ideal inductors have completely imaginary/reactive voltages? What about the inductor's current? Is that also completely imaginary/reactive?
Actually, it's funny that you mention that. We had a lab where we had to do exactly this. I'm not sure if our oscilloscope was special, but the leading waveform was the waveform that was on the left. So for example:
the blue waveform is leading.
$$Let\quad \vec { Z } =R+Xj$$
If X>0,then the impedance is lagging (current lags behind voltage).If X<0,then the impedance is leading (current leads voltage or more accurately, voltage lags behind current). If X=0, the current and voltage are in phase and the load is called purely real. If x≠0...
Definition of maximal, greatest, minimal and least elements of a set: http://i.stack.imgur.com/PnI9V.png
Since c is a minimal element but c is not a least element, this implies that there is one element that is not comparable to c. What is that element? What about d and i?
It's been a while since I've dealt with sequences and series. Here is my explanation of sequences and series and let me know if I am right or wrong.
A sequence is just a list of numbers. By convention, we use the letter ##a## for sequences and they are written in a form like so...
I spoke to someone that said that the reason we know humans originated from evolution is because there is no other scientifically possible explanation. I originally thought the reason we knew humans originated from evolution because we had explicit evidence of human evolution. Although now that...
Here is what I originally meant in my question.
I know from Wikipedia that these two circuits are equivalent:
1.
2.
However, I am unsure if these two circuits are equivalent:
1.
2.
Does it matter if the resistor is on top or below a voltage source after doing a source transformation?
According to this picture from wikipiedia, the resistor is on top of the voltage source:
But even if the resistor (Z) was on the other side of the voltage source, it would still be...
Ah, I completely get it now. So for the 2nd picture with R3 in series with the cap (after the diagram is fixed), the voltage of R2 and the cap is 5V, right?
I asked a couple of other people and they said VR and VL are 90 degrees out of phase. Would that be correct? This circuit is not a purely inductive circuit though, right? So they can't be 90 degrees out of phase, can they?
Ah, that makes sense. I was confused why there is no voltage drop across the resistor.
And what will the voltage across R2 be equal to? Wouldn't it be equal to the voltage source since there is no voltage drop across R1?
So VR2 and the capacitor's voltage would equal 10V? No, that...
So the capacitor will only read the same value as the voltage source just as long as the capacitor is in parallel to the voltage source? What if the capacitor is in series with the voltage source? Will it still read the same as the voltage source? Or will the capacitor's voltage be equation to...