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# AC analysis intro 1

Solving circuits with differential equations is hard. If we limit ourselves to sinusoidal input signals, a whole new method of AC analysis emerges. Created by Willy McAllister.

## Want to join the conversation?

• 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. • 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.
• are these voltages or rate of change of voltages? • 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?
• Why inductor is used in the AC circuit? • 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!

Enjoy!

Aaron
• ac signal is the function of voltage or time or current? • 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 , • Why phase difference between two alternating quantities is more important than their actual phases? • 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.
• I have an existential doubt, not about the video but about the alternating current. I do not know where to put the question, excuse me.
Now my question: Leaving away the stationary state, how does the current to go from the positive pole of the source to the negative pole (assuming that the distance is much greater than the wavelength of the signal as in a transmission line for example or a high frequency circuit), if the polarity varies and therefore, the direction of the current also and due to this, the current should be moved same quantity of meters in one direction and the other. So, how the current can arrive to the "final" of the circuit?

I hope someone can help me with this doubt :( thank you very much in advance. • What is meant by positive phase sequence, negative phase sequence, and zero phase sequence in AIR CIRCUIT BREAKER • This is probably a silly question, but at , 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?
(1 vote) • What are the units of A, s and t. Where this equation come from ? What does it mean ?
(1 vote) • The equation is talking about a current, i = Ae^st.

Both sides of the equation have units of amperes.

A is the scaling factor that tells you how large the current is.

t is time in seconds.

s is frequency in 1/seconds, also known as hertz.

As you work through this sequence of videos you will find out the meaning of e^st. When you combine e^st with e^-st you get a sine wave (Euler's formula).