Really Neat Science Page

[MSimon]

I don't like instantaneous tangent as a description. It may be clear to those versed in the field or mathematicians. For newbies it can be confusing.

I do like instantaneous rate of change. It clearly states the important details.

[BenTC]

Some applets that might help.

http://www.slu.edu/classes/maymk/GeoGeb ... tives.html

http://www.plu.edu/%7Eheathdj/java/calc1/Deriv.html
http://www.plu.edu/~heathdj/java/

[EricF]

Okey doke, just want to make sure I understand this.
C is the variable for capacitance, and L is the variable for resistance? (I tried googling but couldn't find them anywhere)

-You are able to have a current with no voltage when there is no resistance in the conductor, because there is no push force (voltage) necessary to get the electrons to flow?

-Any resistance results in a voltage because the current is no longer flowing freely.
-If the resistance is too high you get a voltage without a current?

What I am fuzzy on is the consequence of a voltage in and of itself. I realize now that a current in and of itself produces the field lines of magnetic force. What are the effects of a voltage without a current?

[MSimon]

L is for inductance.

C is for capacitance

R is for resistance

V (or sometimes E) is voltage

I is for current

All electric effects are strictly current (charge really) based. No charge - nothing is happening. Electricity is charge based. Voltage is just the result of charges moving or charges collected.

[MSimon]

Now if you really want to get deep (not necessary at this point in your education) magnetic and electric fields are duals of each other dependent on your frame of reference.

Feynman explains it well in his 3 book Physics Lecture set. Books 1 & 2 esp. Book 3 is quantum physics. not necessary at this point in your education.

[BenTC]

Okey doke, just want to make sure I understand this.
C is the variable for capacitance, and L is the variable for resistance? (I tried googling but couldn't find them anywhere)

1. You are able to have a current with no voltage when there is no resistance in the conductor, because there is no push force (voltage) necessary to get the electrons to flow?

2. Any resistance results in a voltage drop because the current is no longer flowing freely.

3. If the resistance is too high you get a voltage without a current?

4. What I am fuzzy on is the consequence of a voltage in and of itself. I realize now that a current in and of itself produces the field lines of magnetic force. What are the effects of a voltage without a current

1. Correct.

2. Yes, but see correction of terminology.

3. Yes. An air gap between two conductors is an example of the resistance being too high for a current to flow.

4. In some respects the following might be a bad analogy, but does give some insight. It relies on the following:

• Current is said to "flow" (actually its the charge that flows) Consider water particles equivalent to electrical charge.
• Another name for voltage is "potential" It is the amount of push available.
• Lifting a physical object against gravity rasies its potential.

Consider water sitting high up in a dam with a pipe running down and then pointing horizontal. When the pipe is open, the high potential of the water at the top of the dam pushes the water particles to flow down the pipe and shoot out sideways at the bottom. When the pipe is closed, there is no flow, but the water at the top of the dam retains its potential.

Further, consider a small pipe (2mm) versus a large pipe (10cm). The large pipe will shoot water out sideways further than the small pipe. The smaller pipe reduces the ability of the water to be pushed through it. It has more resistance. The drop in potential along the small pipe is greater than the large pipe, so the water exiting the small pipe has less push than the large pipe, and so doesn't go sideways as far.

[BenTC]

Note that (ideal) inductors and capacitors do not have any "resistance." In place of the term "resistance" the term "reactance" is used, which is a measure of the degree to which the element opposes an alternating current/voltage - at a particular frequency (such as 50Hz).

-------------
Btw, from memory I think you will find the following interesting, although the computer I happen to be using right now doesn't have Java to be able to check.

http://www.falstad.com/circuit/e-index.html

[EricF]

thanks

[BenTC]

http://www.falstad.com/circuit/e-impedance.html

In case your wondering about the statement "The impedance has the same magnitude in each case, but different phases."

CASE 1
Resistance R=100 ohms
Reactance of inductor is X = 2(pi)(f)(L) = 2(3.142)(80)(0.34446) = 173 ohms.
Impedance is Z = SQRT( R^2 + X^2 ) = SQRT( 100^2 + 173^2) = 200 ohms

CASE 2
Resistance R=200 ohms
There is no reactance X=0 ohms
Impedance is Z = SQRT( R^2 + X^2) = 200 ohms

CASE 3
Resistance R=100 ohms
Reactance of capacitor is X = 1 / [ 2(pi)(f)(C) ] = 1 / [ 2(3.142)(80)(0.0000115) = 173 ohms
Impedance is Z = SQRT( R^2 + X^2 ) = SQRT( 100^2 + 173^2) = 200 ohms

The graphical representation of these are shown here.

http://www.allaboutcircuits.com/vol_2/chpt_3/3.html
http://www.allaboutcircuits.com/vol_2/chpt_4/3.html

This also is a good summary...
http://www.allaboutcircuits.com/vol_2/chpt_5/1.html

http://www.falstad.com/circuit/e-indmultind.html

Note, on my system there seems to be a slight anomaly with the animations. The left "wire" on the top animation and the bottom "wire" on the middle animation both seem to be moving too fast.

[olivier]

It might help to think of the mechanical analogy: consider the position x of a body of mass m attached to a spring of constant K and a viscous damper of coefficient B.

The force of the spring is proportional and opposed to the position of the body: -k.x
The force of the damper is proportional and opposed to the speed of the body (the derivative of the position): -B.v
For a free mass you have:
m.dv/dt + B.v + k.x = 0, with v = dx/dt
Now consider a series RLC circuit:
L.di/dt + R.i + q/C = 0, with i = dq/dt
the same differential equation (L, R, C, i, q being equivalent to m, B, 1/k, v, x respectively).

[EricF]

I'll have to ponder this for a while. I'll head out to the bookstore tommorrow. Is there anything specifically from Trig (I'm up to graphing the trig functions) that I need to focus on to understand derivatives and integrals?

thanks

Hi Eric
I highly recommend "The Calculus Tutoring Book" bu Carol Ash
Excellent but low key. Like a good friend explaining calculus while writing and drawing on a sheet of paper.

It should be here next week.