Question 1

I think the right-hand side of the equation should be  dVin/dt if you define Vin as the voltage.  And this equation is not KVL; it is the equation for the rate of change of voltage.

Accepted Answer

at Ikchen9699 you are right. The equation comes from the eqaution VL+VR+VC = Vin
if we write  the VL,VR and VC as differentials. That looks like that 
L dI/dt + R*I + 1/c *∫Idt = Vin. This equation is called intregro-differential equation because of the integral. To make this kind of equations to a differential equation take the derivative on both sides. Now we have the equitation L d^2I/dt^2 + R* dI/dt + 1/c * I = dV/dt.

Question 2

are these voltages or rate of change of voltages?

Accepted Answer

It really seems like it isn't KVL. When we didnt have any voltage source, the equal of KVL was zero, and if we tried to get the rate of change of the KVL equation, this was equal to d0/dt = 0. So now that the second part of the equation is Vin, we should have d(Vin)/dt, not just Vin. Could we have an explanation over this please?

Question 3

ac signal is the function of voltage or time or current?

Accepted Answer

Hello Samananwar,

Both voltage and current vary as a function of time.

Mathematically you could talk about voltage as V(t) = Asin(2πft + Θ). Here A is the peak voltage, f is the frequency and Θ is the phase shift.

We could make a similar equation for current.

Regards,

APD

Question 4

Why phase difference between two alternating quantities is more important than their actual phases?

Accepted Answer

There really isn't a strong definition of "actual phase". Phase is always a relative measurement between a signal and a reference signal. If we have one AC signal we get to choose what time we label time = 0. It can be at a peak or trough, or where the signal crosses 0 volts. It is an arbitrary choice. When we start to think about a second AC signal, one of the important things is its phase relationship with the first signal. This is what we call relative phase.

Question 5

Why inductor is used in the AC circuit?

Accepted Answer

Hello again Sama!

There are a few ways of looking at this:

First from a radio engineer's perspective: Inductors are your best friend. They along with capacitors allow us to form tuned circuits. These circuits are the building bocks upon which all radio transmitters and receivers are built. Without inductors you would not be able to tune a radio.

From a power supply engineer: If you are using a computer be thankful we have inductors. They are the essential to the construction of power supplies. Inductors and their close cousin the transformer are found everywhere. In fact if you are using a computer you a employing dozens of inductors in the chain of power supplies that take the wall outlet power and convert it to a regulated DC voltage for the main CPU. You will also find inductors in the LED lights that light your room.

Finally, lets see what a power grid engineer has to say: It would be nice if we didn't have inductors but they are everywhere. The large generators at the power plant act as inductors, the power lines have inductance. Yes, a simple wire will act as an inductor! Also, almost every AC motor on the grid acts as an inductor. My job is difficult as I must keep track of and supply the imaginary (aka reactive) power that all of these inductors require. This is where phase comes into the equation. All of these inductors make the delay the phase of the current relative to the voltage. That's OK by me as I can talk about cool things like phasors, real power, reactive power, VARS, VA, symmetrical components, lagging power factor, and my personal favorite the syncrophasor!

Please leave a comment below.

Enjoy!

Aaron

Question 6

This is probably a silly question, but at 5:45, what I see in the parentheses looks like a quadratic expression of the form ax^2+bx+c=0. I am obviously missing something here, as Willy McAllister said it would be extremely difficult to solve. Could someone clarify?

Accepted Answer

Not silly at all. When the quadratic expression is set equal to zero, as you wrote, that's the description of the natural response problem, and it is relatively straightforward to solve (see https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-natural-and-forced-response/a/ee-rlc-natural-response-intuition). However, when you set the equation equal to some non-zero arbitrary input represented by v_in, the math blows up in complexity.  It gets hard because you have to search for a function whose first and second derivatives, and itself, all add up to equal v_in. When the equation is equal to zero (natural response), we know how to do that, the solution is an exponential.. In other cases, it's a big chore.

Question 7

plz see  Professor Shankar's introduction into AC LCR circuits 
your derivations is really confusing , the results are the same but the road leading to them is very hard ,

https://www.youtube.com/watch?v=cS83YUpcEsY

Accepted Answer

I'm glad Professor Shankar's presentation was helpful to you. Every teacher takes a slightly different approach to difficult problems. I will see what I can learn from his presentation.

Electrical engineering

Course: Electrical engineering > Unit 2

AC analysis intro 1

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