Tau-ting a circuit

Today, I arrived a moment late to class.  I'd felt awful leaving the house, better than yesterday, but still with sinuses a-drip and mind a-grog, despite my nearly full 8 hours of sleep.  But fortunately, the god of neat plant conversations smiled upon me. I had a delightful conversation with the landscaper about "manicuring" cacti, which I now know to be one of two plural forms for the word cactus. He was trimming the bottoms of the spiky plant, to give them a less bunchy look.  I tried to find the species name, but I couldn't find it on this cactus gallery, and I'm not that persistent..   http://succulent-plant.com/thumbnails03.html
Now I'm really curious what it was.  The gardener said he didn't know, but that he would find out.  Perhaps I'll see the plant-man again one day. *Cue dramatic mysterious plant music*

Professor Mason thought it prudent to introduce inductors today.  Parallel and Series inductors, and more, what a time to be alive!

We did a bit of basic calculus on inductors.  For instance, did you know that
V = L*di/dt
Well now you do.  And if you do a first order circuit, where a resistor is in series with an inductor, you might find that
V(t) = V_0 * e^(t/tau) where tau = L/R. or T = 1/(RC).
This is the behavior of a first order circuit.

We did a practice circuit with 5V in series with a switch, then in parallel to a pair of resistors and a capacitor.  We modeled the time behavior of the circuit.  We calculated the time constant, tau, to be .015s, and 5Tau (which we will measure with an oscilloscope) to be .075s.

Alex made the circuit today:

We did this in preparation for the lab.


Triggered response of RC circuit, Tau is the time difference between base and plateau, about 80ms. We ran the data and were very close to the calculated Tau.  We found:




We measured the time by reading the oscilloscope, taking the difference between the trigger point and point where the voltage has about peaked.  We observe 10% error, which is really good.  We have to estimate the point where 5Tau is on the oscilloscope screen, which accounts for the marginal error.


LC Circuit Lab type occurence
We moved on from capacitors to inductors. Capacitors are old news, and we move on quicker than a.. hmm what's a good pop culture reference... ah, we move on quicker than United Airlines customer base after their embarrassing "gaffe" last week. Heh, I am clearly the pinnacle of wit.

Recall, inductors are the reciprocal of capacitors.
T = RC (caps) = L/R (inductors)

We did a practice example.  We're going to find the value of the inductor Mason gave us based on that diagram.  We're going to measure 5 Tau, and calculate backwards to find the size of the Inductor.

We adjusted our settings, and found 5 tau = 5 micro seconds.  Therefore, Tau is 1 microsecond, and we can solve backwards to find the inductance. Given a 1kOhm and 2.2kOhm resistor in parallel, the equivalent resistance was 687 ohms, and we find the inductor is about .67mH.  Science Bitches!
*I'm getting my energy back, definitely going running today...Caffeine is magic~*