AC Circuits / Alternating Current

In summary, the conversation discusses the topic of AC circuits and understanding impedance. The individual is looking for derivations of alternating voltage and current formulas, but is only able to find the equations in their textbook. They are directed to study electricity and magnetism and are provided with resources such as video lectures and articles to help them understand the concept better. The individual is also given a basic explanation of why alternating voltage is a sine wave and is encouraged to watch a specific lecture for a more in-depth explanation.
  • #1
woodentsick
6
0
Hi, PF :)

I was self-studying AC circuits, and my main goal right now is to understand impedance. However, before that, I was wondering how one would derive the formulas for alternating voltage (and current), namely [URL]http://upload.wikimedia.org/math/5/a/0/5a0ecaa1432c6cdce653a943b4962a21.png[/URL]

The textbook I borrowed from the library does not have derivations of the formulae :( They just write down the actual equation...

Thanks so much!

Woodenstick
 
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  • #2
It is so because alternating voltage is created by Electromagnetic Induction, basically by spinning a coil inside a magnetic field. This delivers voltage in the form of a sine wave.

If you want to understand how it is created, study "Electricity and Magnetism".
If you don't know it yet, I highly advice you to do so. It is a beautiful theory and very practical!

Great video lactures from Prof. Walter Lewin (MIT):
http://ocw.mit.edu/courses/physics/8-02-electricity-and-magnetism-spring-2002/video-lectures/

http://en.wikipedia.org/wiki/Electromagnetic_induction
 
  • #3
Hey, thanks for your reply!

I looked at some of the MIT videos, and they were very informative, but as far as I know they don't cover the derivations of the equations for alternating current/voltage :(
 
  • #4
woodentsick said:
Hey, thanks for your reply!

I looked at some of the MIT videos, and they were very informative, but as far as I know they don't cover the derivations of the equations for alternating current/voltage :(

I've already gave you a basic explanation why it's a sine (because it's spinning) :)

gomunkul51 said:
It is so because alternating voltage is created by Electromagnetic Induction, basically by spinning a coil inside a magnetic field. This delivers voltage in the form of a sine wave.

But nevertheless Prof. Lewin does have a rudimentary explanation in one of the videos and I think this is exactly what you are looking for.

http://ocw.mit.edu/courses/physics/8-02-electricity-and-magnetism-spring-2002/video-lectures/lecture-17-motional-emf-and-dynamos/

P.S. congratulations! you will know how electricity is created.
 
  • #5


Hi Woodenstick,

It's great that you are self-studying AC circuits and specifically focusing on understanding impedance. To answer your question about deriving the formulas for alternating voltage and current, it would be helpful to first understand what AC circuits are and how they operate.

Alternating current (AC) circuits are electrical circuits where the current and voltage alternate back and forth between positive and negative values. This is in contrast to direct current (DC) circuits, where the current and voltage remain constant. AC circuits are used in many applications, including power transmission, household appliances, and electronics.

In order to derive the formulas for alternating voltage and current, we need to use the principles of Ohm's Law and the concept of impedance. Ohm's Law states that the current in a circuit is directly proportional to the voltage and inversely proportional to the resistance. In AC circuits, we also have to consider the effects of capacitance and inductance, which contribute to the overall impedance of the circuit.

Impedance is the measure of opposition to the flow of alternating current in a circuit. It is represented by the symbol Z and is measured in ohms. In AC circuits, impedance is a combination of resistance, capacitance, and inductance and is calculated using the following formula:

Z = √(R^2 + (Xc - Xl)^2)

Where R is the resistance, Xc is the reactance of the capacitor, and Xl is the reactance of the inductor.

Now, to derive the formulas for alternating voltage and current, we can use Ohm's Law and the formula for impedance. We know that in a circuit, the voltage is equal to the current multiplied by the resistance:

V = I * R

However, in AC circuits, the current and voltage are constantly changing, so we need to consider the impedance in our equation. Using the formula for impedance, we can rewrite Ohm's Law as:

V = I * Z

Substituting the formula for impedance, we get:

V = I * √(R^2 + (Xc - Xl)^2)

This is the formula for alternating voltage. Similarly, we can derive the formula for alternating current by rearranging the equation to solve for I:

I = V/Z = V/√(R^2 + (Xc - Xl)^2)

I hope this helps you understand how the formulas for alternating voltage and current are derived. Keep
 

1. What is an AC circuit?

An AC circuit, or alternating current circuit, is a type of electrical circuit that uses a current that periodically reverses direction. This is in contrast to a DC circuit, which uses a constant flow of current in one direction. AC circuits are commonly used in homes and buildings for powering appliances and electronics.

2. How does an AC circuit work?

An AC circuit works by using a power source, such as a generator, to create an alternating current. This current then flows through a circuit, which typically includes components such as resistors, capacitors, and inductors. These components can be arranged in different ways to create different types of AC circuits, such as series or parallel circuits.

3. What is the difference between AC and DC circuits?

The main difference between AC and DC circuits is the direction of the current flow. In AC circuits, the current periodically reverses direction, while in DC circuits, the current flows in one direction only. Additionally, AC circuits are generally used for high-power applications, while DC circuits are commonly used for low-power applications.

4. What are the advantages of using AC circuits?

There are several advantages of using AC circuits. One advantage is that AC current can be easily stepped up or down using transformers, allowing for efficient transmission of electricity over long distances. Additionally, AC circuits can be easily converted to DC using a rectifier, making it possible to power a wide range of devices.

5. What are some common applications of AC circuits?

AC circuits have a wide range of applications, including powering household appliances, lighting, and electronics. They are also used in industrial settings for powering machinery and equipment. Another common application is in the transmission and distribution of electricity through power grids.

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