Experiment with complex numbers

[britneyfan]

My friend and I have to do an experiment for Physics. We chose complex numbers and we wanted to experiment with AC power. Our teacher said the experiment should consist of measurements so that we would have actual results and get a conclusion out of that or something like that.
Does anyone have any suggestions to what kind of experiments we can do?

We have to hand it in by Friday next week (21 January 2005) so can anyone help us?

 

[DaveC426913]

I'm afraid I can't help, but I would be very interested in reading about your progress.

 

[britneyfan]

well thanks i'll let you know

Anyone else?

 

[Galileo]

I think the easiest experiment is to make a low-pass filter and/or a high-pass filter with a resistance and a capacitor and an AC voltage source.

Calculate what the gain $$U_{out}/U_{in}$$ of the filter is as a function of the frequency and compare your measurements with the theory.

 

[Gonzolo]

You need to do an experiment and you "chose complex numbers"?

What kind of equipment do you have available? Wave generators and oscillosopes are rather important for AC experiment. What level of education is this?

 

[britneyfan]

OKay, here's what we did (we've already did the experiments, and now have to write the report about it, which has to be handed in TOMORROW!):

We made 2 electric circuits, one with an capacitor and resistance, the other with a self (i don't know if that's the right name, but it's that thing with self-induction?) and resistance, on AC voltage. We measured the U and I and Ohm on everything. Then we connected an oscilloscope to measure the U on the capacitor and another wire which was also connected to the same oscilloscope we measured the resistance. On the screen we saw 2 sinus-waves, with a phase difference. We did the same with the self.

Well, we have some results, but we don't know what to do with them. As in, what was the purpose of our experiment? We need to have an "main experiment's question" but we don't know what. We thought we'd do something with the phase change... but it's difficult...

Can anyone help?

btw: we're seniors from high school, in the Netherlands

 

[Goalie_Ca]

How much calculus do you know? (the more the merrier!)
Looking at those pictures you should have enough data for the low pass and high pass filters. But, what worries me is what you chose for the time constants. What you need to do is plot the voltage across the resistor vs. the voltage of the ac-source. What magnitude of phase shift are we talking about?


btw. the symbol for a capacitor is two parallel plates " | | ", because that's what it is.
It isn't U, it's V for Voltage.

Here's a low-pass filter. Unfortunately the math to explain it can be difficult through ODE's, or laplace. I suppose I might try explaining it using phasors.

Crash Course in Phasors...

In: Vs*cos(wt+theta)
Out: Vm*cos(wt+phi) = Acos(wt)+Bsin(wt);
Vm = sqrt(A^2+B^2) , phi=arctan(-B/A)
exp(sqrt(-1)*theta) = cos(theta)+sqrt(-1)*sin(theta)

phasor typically represented as:
V=Vm /_ phi

capcitor is now called an impedance and treated like a resistor.
It's impedance is 1/(sqrt(-1)*w*c). So now you have a simple voltage divider circuit.
Vo/Vin = 1/(1+sCR) where s=j*w, and j = sqrt(-1) (we don't use i because i is current.. oddly enough there are more complex numbers that i2 = j2 = k2 = i j k = -1. So it's not that j. )

when the output over input magnitude is 1/sqrt(2) you should get -45 degrees phase shift.

Hopefully you got that. If you didn't... well electronics are a lot harder than most people think.