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3
Part A – Build Your Own Circuits (kind
of)
 Overview
For this activity I’ve decided to switch things up a bit, instead of me doing all the lab work and you
simply seeing the results I get it would be nice if you got to do something too, luckily some nice folks
at the University of Colorado made a nice repository of various simulations in different subjects and
one particular subject was DC Circuits, so you will be able to build series and parallel combinations of
circuits
So for this first part you’re going to actually build a series of circuits, and calculate the equivalent
resistance of them, and then calculate what it should be and just verify you get the same results.
Also many of you will like this next part, absolutely no uncertainty calculations at all! Since the
simulation uses “idealized” settings if the value on a resistor is 100, it means it’s exactly 100. So
instead you’re going to just compare the values in the simulation versus your calculation and they
should match up very close to one another (possibly a bit off due to rounding errors).
 Instructions
DC Construction Kit (https://phet.colorado.edu/en/simulation/circuit-construction-kit-dc) is the
simulation that you’ll be using, it’s programmed into HTML5 which basically mean any web browser
can run it without any 3rd party programs (e.g. Java, Flash, etc). I would suggest doing this on a
computer, or a tablet if possible, I did try it on my phone and while it works, I just could not find a way
to zoom into anything so it was a bit hard to manipulate things, so take that as you will.
Now feel free to play around with it as it’s not too difficult to figure out how to do, but I did make this
video showing how to work it, and I worked through the series and parallel examples I did earlier.
You’ll have to calculate the equivalent resistance via Ohm’s law using voltage and current, the video
does show you how to do that as well.
DC Circuits App Instructions
For each setup
A. Build it in the DC Circuit simulation program finding the resistance, use Ohm’s law with voltage
and current
B. Calculate it theoretically, showing your work for each one.
C. Verify that what you get is the same for both, or at least so close that you can argue that
rounding off a decimal is what caused the small variation
D. Attach the solutions to the assignment page a little later on.
For the simulator you will need to add a battery since there’s no way to directly measure
resistance, no Ohmmeter, just hook one side of the battery to one end of the resistor bunch, and
the other side to the other end
You won’t need to use the voltmeter probes to measure voltage, whatever the battery voltage is
will be the total voltage across all your resistors
Measure current anywhere but between resistors, near the battery is a perfect spot, we want to
measure all the current that goes through the all the resistors not what gets split off if there’s a
junction.
Drawing squares for resistors is a lot easier for me to whip up these drawings for you, so just realize
I’m being lazy in my diagram. And for each them the resistances are the following
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Part B – The Battery
 Overview
When you think of a battery the first thing that comes to mind may be a cylindrical shaped object with
bump on one end that you’d put into a remote control or flashlight, or maybe you think of something
like a car battery which is a large rectangular block with two bumps on the top. Regardless of the
type of battery they operate in similar ways, there’s some sort of “chemical soup” plus a cathode
(positive) and an anode (negative). Now I’m not going to pretend that I know how the chemistry
works inside a battery but regardless of how it works it’s not a “perfect” process, when you hook up
the battery to a circuit so that it needs to provide power it creates a resistance inside of the battery
due to how the “soup” behaves.
We can actually model the battery like this.
Unfortunately that resistance is not one that you can measure directly, so what we’ll attempt to do is
indirectly find a way to measure this resistance using the tools you’ve learned for this week’s activity,
as well as last week’s activity.
Setup
So we’re going to create a setup similar to what we did last week when did resistance curves with a
couple small changes.
The first difference comes right after the battery, this is a switch, it really doesn’t affect the circuit
except to provide an on/off functionality to it. The reason why the switch is put in is because a
battery does have a limited supply of power it can provide and the switch allows me to set up
everything without draining the battery and when I’m ready to take data I push down on the switch
to get my data then release the switch
The other difference is the resistor symbol with an arrow through it, the arrow typically means
“variable” so in this case a variable resistor. The type of variable resistor that I’m using here is
called a decade box, this allows me dial in resistance 0 to 99,999 ohms in increments of 1 ohm.
In the picture below there are a number of knobs on it, and each knob changes a particular
decimal, the bottom knob changes the ones place from 0 to 9ohms in 1 ohm increments, the
second knob changes the tens place from 0 to 90 ohms in 10 ohm increments, etc. so if I wanted
a 43 ohm resistor I’d dial the second knob to 4, and the first knob to 3.
Now the battery here has been modified from a traditional battery, first the non-important parts are
the plugs put to the top so that students (or me) can easily plug in cables, but the more important
part (as in don’t forget this is there!) is that there is a limiting resistor put into the top of the battery the
purpose of which is to prevent students (or me) from overloading the battery by accidentally putting
too little resistance across it which can happen if the decade box is set to 0. This resistor however is
real and something we can measure, listed below, but we will model this resistor as “internal” since it
is physically between the positive and negative connection points.
Now with everything squared away, I’ll just redraw my circuit diagram so all the “resistances” are
modeled and it’s easier to visualize.
In case you’re wondering, the purpose of the variable resistor is to take the place of the variable
power supply that we used last week. A battery has a set voltage that it puts out which can’t be
adjusted, so the variable resistor allows us to adjust the voltage that gets to the “internal” resistances
(Rbat & Rlim). This all by Kirchoff’s laws
If we increase the resistance to the variable resistor we also increase the voltage drop across the
variable resistor, since the output of the battery voltage is constant that means a smaller voltage drop
across the internal resistances from the battery and limiting resistors. So effectively we made a
variable voltage source for the internal resistance, and can work it very similar to what we did last
week (even if some of you hated it).
Data
Below is a table of resistance dialed into the decade box as well as the voltage that was read, I know
I said the decade box changes in 1 ohm increments however for sake of accuracy I actually
measured the resistance at each setting so that when you calculate the current you get a more
accurate value. Please note that for this activity we are not going to worry about uncertainties at
any step… I can almost hear the cheers now (and you haven’t even read this yet!)
Rx(
)
Vx(V)
5.2 1.969
6.1 2.209
8.1 2.628
9.0 2.789
10.9 3.078
12.0 3.211
13.9 3.427
14.9 3.531
19.8 3.913
29.9 4.40
49.6 4.88
1. Make a table using the data above, add another column and find the current at each resistance
point
2. Make a plot of V vs I, this is different than what you did last week with I vs V
3. Find the equation of the line that is formed
4. Using that equation find the total internal resistance of the battery, hint: don’t freak out if you see
a negative number just treat it as if it’s positive and try to find out why it’s negative in the
discussion
5. The limiting resistor is 7.8 ohms, use that to find the battery’s internal resistance
6. Turn in your work on the assignment page (next one)
Now at some point you might be thinking to yourself “but we’re reading the voltage across the
variable resistor, not the internal resistors how does this even work?”, this is where you need to think
outside the box, yes you are reading the voltage across the variable resistor but you also are reading
the voltage across the battery and all the resistances of it, stare at the diagram for a while if you don’t
get why, and if you still don’t understand why think Kirchoff’s voltage rules. This will be helpful for
answering one of the discussion questions.

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