What is the Amplitude of an Electron's Oscillation in AC Household Current?

[Abelard]

Homework Statement

In a typical household current, the electrons in the wire may have a drift speed of 1.3×10−4 m/s. Actual household current is not a direct current, but instead is an alternating (oscillating) current. (If you have ever received an electric shock from an outlet, you have felt this rapid alternation as a painful vibration. A safe way to see the alternation is to wave your fingers rapidly in front of a fluorescent light, and observe the stroboscopic stutter-silhouette that they form.) You can model the motion of each conduction electron as simple harmonic motion, with a frequency of 60 Hz. The drift speed is the maximum speed, what the speed would build up to if the electric field were applied continually, as in the case of direct current. What is the approximate amplitude of an electron's oscillation?

Homework Equations

1/T=f or 1/f=T

The Attempt at a Solution

So 1/60Hz=0.1667sec = T Then period is a time of complete cycle, so 0.1667/4sec is one amplitude. Then 0.0041667sec * drift speed = 1.3e-4* 0.004167=5.42e-7 m.


But that wasn't the answer.

 

[gneill]

The applied electric field that is motivating the electrons is a sinusoidal function of time. Try writing the velocity as a sine (or cosine) function of time. If you do that, how would you find the position of an electron as a function of time?

 

[Abelard]

Asin(2pi*x/lambda-2pi*f*t)=y as a function of x and t. and you're not helping me yet.

 

[gneill]

That's a formula for traveling waves. It's not what you want. There should be no dependence on distance (x) in the argument.

Have you studied simple harmonic motion?

 

[Abelard]

I supposed I did but you didn't explain why there's no distance dependence.

 

[Abelard]

Electrons have dual nature of wave and also of particle. Did you study anything about electrons and current and the fact that it moves in a zigzagging path? It's a wave as well. But if you say so, which equation are you talking about and if you know it why not put it on your pose unless you're just showing off you "intelligence."

 

[gneill]

Electrons have dual nature of wave and also of particle. Did you study anything about electrons and current and the fact that it moves in a zigzagging path? It's a wave as well. But if you say so, which equation are you talking about and if you know it why not put it on your pose unless you're just showing off you "intelligence."

The idea is to get *you* to think about how to solve the problem and reach a solution, not to simply give you the answer. Giving you an answer now won't help you when you face similar problems on an exam.

 

[Abelard]

Fortunately it does help me.

 

[gneill]

Fortunately it does help me.

Well, good luck with that. I wish you success.

 

[Abelard]

OK I got it. The amplitude must be 3.448e-7m. Vmax=-A*2pi*f

 

[Abelard]

I apologize for what I said since I finally got the answer.

 

[SammyS]

OK I got it. The amplitude must be 3.448e-7m. Vmax=-A*2pi*f

Just a thought:

The electron drift speed of 1.3×10−4 m/s refers to the "typical household current".

When comparing AC & DC, a typical DC current generally corresponds to the root-mean-square (rms) AC current, I_rms. The amplitude for a sinusoidal wave form is √(2) times the rms value.

It may be that your answer for the electron amplitude should be multiplied by √(2) .