General Feedbacks:
Most of these are very good so far, but I am going to complain again and again about
these units!!! We’ve got them reported pretty well now in tables and graphs and such,
but still I need to see those units on the slopes you report too! When you report a slope
it does have units too. The units on a slope are are
/
When you write this lab report please make it as detailed as you can as to what you
did, so that anyone can read it and reproduce your work. This means that I want to
know everything you set up, how you varied any parameters, and what you held
constant. This is critical. This does not mean, however, that you should rewrite this
document for another reader. This lab guide is intended to push you in the right
direction of inquiry and to more or less bullet point the things I am looking to see in
your report. You can and should report the general procedure, along with any
equations and theory that are used (every plot has a physics equation it relates to, that
is essential). I am really after the analysis though. When you write the report, report on
what you did and what you found. What I really want to read is your report on your
findings, not an edited version of a document that I wrote. Nothing from this document
should be copied and pasted into your lab report. Use it to help collect data and take
notes, but probably not to write the report.
Make sure to take and give a screenshot of each different lab space you use. Mostly I
need it so if something is wild in your data I can look and try to see what went wrong.
Please try to keep your data tables, the graphs it belongs to, and the relevant text
about that experiment together. Do not just drop all your graphs down, then all your
tables down, and then a giant block of text. Spread that text out among your data and
images, so that when someone goes through it they can look at your words and the
visuals at the same time without all sorts of page flipping (scrolling).
At the very end of the document a conclusion with a quick results summary for all of
the parts is nice. Usually the conclusion is where I start, just to get a general idea of
how the lab went for you.
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Introduction:
In this lab we want to use the ideas we have about electromagnetic induction, to
understand the properties of inductors and solenoids in general. We will look at how
inductors work in different types of circuits.
In general electromagnetic induction describes how an EMF (ε)
potential is created when the magnetic flux (ΦM) through any loop
changes. That EMF drives charge around the loop in the form of a
current. The flux change rate and the EMF are related as shown,
where N describes how many times the loop winds (called turns).
This is Faraday’s Law.
All of the geometry of the loop and the number of turns is wrapped
up into what is called the inductance (L) of the loop. When the EMF
is considered in terms of the inductance, we find it depends on the
rate that the current changes in time, like shown to the right.
As you can see, there is only a voltage across an inductor when the current through it
is changing. If the current is constant, then there’s no voltage induced. It requires
change. Usually, in a circuit, to make a change you flip a switch. Immediately, there is
a lot of change, as the current flips from zero to on, so the induced voltage can be big.
But then the system settles down to a constant steady state in current, dropping the
induced voltage down to zero.
When you stick these things with other circuit elements like capacitors and/or resistors
they behave in interesting ways, a couple we will look at here.
The Lab Space:
You can find the lab set up right here! Use the RLC mode.
Circuits with Inductors
There’s two parts to this lab.
Part 1: LR Circuits
Part 2: LC Circuits
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Part 1: LR Circuit
Compare a circuit which powers a light bulb
with and without an inductor. In a more useful
circuit the light is replaced by something you
are using to purposefully consume power.
First build a DC circuit with just a light bulb and
a resistor in parallel. Set the battery to 50V, the
light bulb at 100Ω and the resistor to 10Ω. Stick
a switch by the battery so you can control the
power source. (RIGHT)
This is just a simple circuit with two resistors in
parallel. Before you flip the switch, note and
report
● What is the voltage across and current
through the light bulb?
● What should the voltage and current be
after you flip the switch?
Now flip it and, and check that you were right.
● Screenshot your circuit.
Use the switch to turn off the battery.
Now put a 50H inductor in series with the 10Ω
resistor (with the switch still open). (RIGHT)
When you flip the switch the inductor will
“charge” which you can notice if you watch the
current through and voltage across. Notice
some things and report
● In charging, the voltage across the inductor decreases from 50V to 0V.
● Meanwhile, the current raises from 0 to what value? Based on the 10Ω resistor
here in series with the 50V battery. Why does that current maximum make
sense?
Flip the switch to disconnect the battery and observe/report. Some good ideas are…
● Does anything interesting happen with the voltage? Why does it do that?
● How does changing the inductors L value affect the charge/discharge timing and
max voltage? (data/plots are a good way to test this)
● Be sure to compare the power drawn by the bulb with and without the inductor.
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Part 2: LC Circuit
Here we use a capacitor and an
inductor in parallel connected to
the DC battery with a switch, as
shown on the right. You have to
put a resistor by the battery, or
else you’ll get a short circuit and
we don’t want to start any digital
fires! Keep R pretty small; we are
just using it to avoid melting our
wires.
Pick a voltage, capacitance and inductance that you want, maybe somewhere in the
middle ish of the available ranges. Flip the switch to “charge” the system. You’ll know
you are there when all of the voltage in the circuit is dropped on the resistor. Here all of
the energy in the system is stored in the magnetic field of the solenoid’s constant
current.
When you flip the switch and disconnect the battery, the system will behave as an
oscillator pushing the charge in one direction and then the other. The inductor
discharges into the charging capacitor, then the capacitor discharges into the inductor.
And on and on.
When you measure the voltage and/or current here you will see that it does behave
sinusoidally. In fact, the angular frequency of the oscillation is well known, as is the
period of oscillation. The period, T (which you can measure with the stopwatch tool) is
related to the capacitance C and inductance L with
T = 2 π (LC)½
● Take data and to confirm this relationship between the period T and the values of
L and C. Try to take enough data to cover the full range of L and C space.
(Hint: I think it’s easier to put T
2 on the y axis, to undo the square root like
T
2 = 4 π
2 LC
You can choose how you want to plot it, just demonstrate this relationship completely
in your data and analysis. This means comparing slopes to constants in some way.
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