to do listCalculate the equivalent resistance of all 5 setups for part A, making sure to show your workCompare those results to the DC Circuit simulation results you built of each circuit, make sure to show your work here what was your voltage and current to get the resistance you’re comparing against, this can be as simple as stating that the numbers are the same or close enough.For part B turn in your V vs I plot with the equation of the line of the data, you do not need to use LINEST nor find uncertainty.Show how you find the total internal resistance (from battery and limiting resistor) then how you find just the battery’s resistanceand discussiondiscussion: Analysis of Battery DataDon’t stress out too much if you can get all of these questions, they’re here to try and get you to think more about what you’re seeing with your data and how to interpret it, that is to say I want you think more about “what equation do I use” when you see this data.So a battery is limited to how much current it actually put out,, that’s to say if you had a AA battery that has a voltage of 1.5V, if you put a wire with very little resistance from the positive to negative you won’t draw so much current that the wire melts (although a microfine thin wire may), there is a maximum current it can put out, this is called the short circuit current, I S C, and it is measured when the voltage is zero, that is to say zero resistance so zero voltage drop. Using your data what is I S C of this battery?Much like the short circuit current there is an absolute maximum voltage a battery can put out, where there’s no load on on the battery (i.e. it’s not hooked up to anything), this is called the open circuit voltage or V O C which occurs when no current is being pulled. What is V O C of this battery?I told you to ignore the negative sign in part B for your data, why is the sign negative at all?Lab

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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