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UTD physics - Fall 2023
Electricity III
Goals
Define the concept of obstacle Determine how obstacles combine when in series and in parallel. Expand model of electricity to include effects of obstacle size
Equipment
♦ 3 rechargeable ‘D’ cells. ♦ Battery holders ♦ 3 rheostats; 2 short & 1 long. (Each rheostat uses 30 A.W.G. Kanthal A1) ♦ #48 bulbs - marked; white bulb-holders ♦ #14 bulbs – unmarked; blue bulb-holders (paper cup) ♦ #48 bulbs – unmarked; blue bulb-holders (paper cup) ♦ 1 Meter stick ♦ One 22 Ohm or 20 Ohm resistor; loose (paper cup) NOT attached to dual binding post! ♦ 8 alligator-to-alligator wires ♦ 2 (long) banana-to-alligator wires ♦ 1 (magnetic) compass
Groups will share standard obstacles including 3 spools of insulated wire.
Verify that you have all the equipment listed. Notify your TA if anything is missing.
Introduction
So far, the Model of Electricity is :
- Electricity flows in electric circuits.
a. If two bulbs are identical and the same flow of electricity passes through them then they will light with the same brightness (and vice versa.) The brightness of a bulb increases if flow through it increases (and vice versa) b. No flow is used up by components as it goes around the circuit c. The flow through components that are wired in series is the same d. The flow going into and coming out of a branch (made of components that are in parallel) is the same.
At the end of electricity II, we made (but didn’t test) the hypothesis that “ Other factors being equal, the
size of the flow increases if a component offers it a smaller obstacle (and vice versa)”. At that time, we imagined that the battery responded to the obstacle presented to it by changing the size of the flow; the
UTD physics - Fall 2023
battery sends a large flow if the obstacle is small, but sends a smaller flow if the obstacle is large. If the circuit consists of several obstacles, then somehow the battery ‘senses’ the total size of the obstacle (also called ‘the equivalent obstacle’) and sends the circuit a flow of an appropriate size. For example, the following circuit diagram shows two bulbs in parallel with each other.
H
B
Network A
But the battery doesn’t ‘sense’ the details of the circuit. All the battery ‘senses’ is that network A is connected to it. Somehow it figures out the appropriate (total) flow to send to the network so that when the flow splits up, the flow through bulb H and bulb B is ‘correct’ given the different obstacles that they present. The ‘correct’ flow will have something to do with the total obstacle that network A presents (if the hypothesis above is correct and if the idea of ‘obstacle’ is a useful one.)
This lab will measure the size of an obstacle (by comparing it to a length of Kanthal wire.) Once we can measure the size of an obstacle, we will figure out how to combine obstacles to find the equivalent obstacle that is ‘sensed’ by a battery.
This approach can only work if we can find a means of measuring the size of an obstacle. Our observations so far have not included much quantitative measurement. Perhaps that is as it should be: Physics is often presented as if it were about nothing except measurements and the use of memorized formulae. Measurement (or calculation) usually serves to add increased precision to answers that we already know. That is not to dismiss the use of measurement and calculation but to see these techniques in perspective. It is important that we have at least a rough idea of what is happening before we jump into precise measurements or calculation.
One possible way of measuring obstacle presented by an object would be to discharge a charged capacitor through the object and a certain bulb. We might expect that the time that a bulb glowed would be a measure of the obstacle presented. Suppose that the obstacle presented by an object is very large. A capacitor is charged and then is put in the following circuit;
UTD physics - Fall 2023
external circuit with alligator clips.
Length of wire being used
To external circuit
Electricity will only flow through the wire between the clips. Obstacle 𝐻𝐻 is the length of Kanthal wire that is between the clips. This device is a very simple rheostat. (You have three rheostats. The biggest of these is just a long length of Kanthal wire that is held in place by either hooks or screws.)
Some of the newer rheostats are made of clear plastic. The smaller plastic ones allow a connection to one end of the wire by way of a banana connector. The other end is (closest to the spring) needs to be connected using an alligator clip as in the case of the wooden rheostats. For these rheostats, electricity will only flow through the wire between the clip and the end of Kanthal wire that is connected to a banana
terminal. Obstacle 𝐺𝐺 is the length of Kanthal wire that is between the clip and banana terminal.
Either rheostat allows us to measure the length of Kanthal wire with a meter stick.
Suppose that the alligator clips are moved so that bulbs D and E have the same brightness_. (Remember that the size of obstacle H is being controlled by this length of wire.)_ To answer the following question, you will need a statement from the model of electricity at the start of the Introduction.
4. Compare the flow through bulb D with the flow through bulb E****. (Instead of quoting the relevant statement from the model of electricity, just include the label; 1a, 1b or 1c in your answer.) **[2]
- Use your previous answer to compare the flow through obstacle** 𝐺𝐺 and obstacle 𝐻𝐻**. [1]
- Use the hypothesis (underlined near the beginning of the introduction) to make a statement** about the relative sizes of obstacles 𝐺𝐺 and 𝐻𝐻. [1]
Be very careful that you understand how circuit 2 operates. Similar circuits will appear in these labs for the next few weeks.
Suppose that we assume that the hypothesis of ‘obstacle to the flow’ still makes sense after we have tested it. Consider the following circuit.
UTD physics - Fall 2023
A
Circuit 3
L
B
C
The two bulbs are identical. Suppose that the alligator clips are moved so that the rheostat presents an obstacle of the same size as conductor B.
7. How will the brightness of bulb A compare with the brightness of bulb C****? Explain. [3]
We’ll use rheostats to build circuits that measure the sizes of obstacles during the experiment. We’ll see if the hypothesis of “obstacle to the flow” continues to make sense.
UTD physics - Fall 2023
D
Circuit 1
LR
E
Adjust the length of Kanthal wire, 𝐿𝐿𝑅𝑅, so that both bulb D and bulb E have the same brightness. Please be
careful when doing this. Sliding the alligator clip doesn’t work. When the alligator clip slides most easily, it doesn’t make good contact with the Kanthal wire. To get good contact, make sure that the jaws of the alligator clip hold the Kanthal wire. To move the clip, unclamp it, move it to a new position and then release the clip so that the jaws hold the Kanthal wire.
1) After making this adjustment , what can you say about the flow of electricity through the bulb D relative to the flow through bulb E****? Explain using a concept from the model of electricity. (Instead of quoting the relevant statement from the model of electricity, just include the label; 1a, 1b or 1c in your answer.) [1]
2) What can you say about the size of the obstacle presented by the carbon resistor relative to the size of the obstacle presented by the rheostat? Explain. (You can use your previous answer to help with this explanation.) Mention any hypothesis that you use. [3]
3) In your report , draw a circuit that can be used to find the obstacle presented by a bulb. (Your circuit can only use apparatus used in this and the previous labs done in this course.) Explain how the circuit can be used to measure the obstacle presented by a bulb. On your diagram, label the bulb that is having its obstacle measured and label any bulbs that are identical.
Show your circuit diagram to your TA before proceeding.
UTD physics - Fall 2023
- Use circuit 1 (and unmarked bulbs!) to measure and record the length of Kanthal wire that is equivalent to the obstacle presented by each of the objects in the first column of table 1. Use one cell as the battery for circuit 1. The objects in table 1 will take the place of the carbon resistor in circuit 1. This will allow you to compare the obstacle presented by them to the obstacle presented by a length of Kanthal wire. After measuring the size of the obstacle, notice the deflection of the compass.
Table 1 Object Size of Obstacle when we use one cell
Size of Obstacle when we use two cells in series
Size of Obstacle when we use three cells in series Carbon resistor
Any spool of wire
alligator-to-alligator cable
incandescent bulb - unmarked
Make a battery that consists of two cells in series. Repeat the measurement of the sizes of the obstacles that are presented by the objects listed in table 1.
- Use your measurements to fill in the second column of table 1. Notice the deflection of the compass.
Repeat using battery of three cells in series.
6) Fill in column 3 of table 1. Notice the deflection of the compass. [5]
7) Compare the flow through the circuit when one cell was used, with the flow when two cells were used. What happened to flow when three cells were used? [1]
There is experimental uncertainty associated with every measurement. Reducing this uncertainty closer to zero is not the focus of building a physical model. Your task is to look for patterns in your results despite the ever-present uncertainty in your measurements.
8) For which objects is the obstacle approximately constant if the number of cells is allowed to change? For which objects is the obstacle not even approximately constant as the number of cells changes? [3]
Have your TA check this answer
UTD physics - Fall 2023
Table 3a Length of Kanthal ( L ) Obstacle presented by two of these lengths in parallel 30 cm
40 cm
50 cm
60 cm
Measure the equivalent length of the obstacle presented by two 30-cm pieces of Kanthal in parallel.
15) Record the results in the first row of table 3a. [1]
16) Repeat for two lengths of 40 cm, 50 cm and 60 cm, recording the results in table 3a. [3]
- Use table 3a to write an expression for an obstacle (called 𝑳𝑳 (^) 𝒆𝒆𝒆𝒆 ) that is equivalent to two pieces of Kanthal of length 𝑳𝑳 (^) 𝟐𝟐 that are in parallel. [1]
In the following diagram, pieces of Kanthal of length 𝐿𝐿 2 are represented by narrow shaded rectangles. The dotted box is imaginary. 𝐿𝐿𝑒𝑒𝑒𝑒 is the obstacle measured by an external circuit outside the dotted box. The size of 𝐿𝐿𝑒𝑒𝑒𝑒 is the same in the next two diagrams.
Going further, imagine that each of the obstacles 𝐿𝐿 2 (in the diagram above), is actually made up of two obstacles (inside the dot-dash lines in the diagram below). Each of the four smaller obstacles has length 𝐿𝐿 4 (in parallel). Each of the four smaller obstacles has length that we’ll call 𝐿𝐿 4 (in parallel). There is a
𝐿𝐿 2 𝐿𝐿 2
𝐿𝐿𝑒𝑒𝑒𝑒
UTD physics - Fall 2023
subscript ‘4’ to remind us that there are four of these lengths! There is no implication about the relative lengths of 𝐿𝐿 2 and 𝐿𝐿 4.
18) Express 𝑳𝑳 (^) 𝟐𝟐 in terms of 𝑳𝑳 (^) 𝟒𝟒. Previously you found 𝐿𝐿𝑒𝑒𝑒𝑒 in terms of 𝑳𝑳 (^) 𝟐𝟐. Use this to express 𝑳𝑳 (^) 𝒆𝒆𝒆𝒆 in terms of 𝑳𝑳 (^) 𝟒𝟒. Show your calculation and explain (in words) what you are doing. [3]
The expression for 𝐿𝐿𝑒𝑒𝑒𝑒 in terms of 𝐿𝐿 4 can be interpreted as an expression for the size of an obstacle 𝐿𝐿𝑒𝑒𝑒𝑒 that is presented by four identical obstacles of size 𝐿𝐿 4. What if each obstacle 𝐿𝐿 4 above was actually made up of two obstacles of size 𝐿𝐿 8.
19) Express 𝑳𝑳 (^) 𝟖𝟖 in terms of 𝑳𝑳 (^) 𝟒𝟒. Use your previous work to express 𝑳𝑳 (^) 𝒆𝒆𝒆𝒆 in terms of 𝑳𝑳 (^) 𝟖𝟖. [2]
The discussion of the previous paragraph allows you to calculate the obstacle presented by several identical obstacles in parallel.
- Write down an expression for an obstacle (called 𝑳𝑳 (^) 𝐞𝐞𝐞𝐞 ) that you expect to be equivalent N pieces of Kanthal of length 𝑳𝑳 that are in parallel. [1]
Show the patterns you have noticed to your TA.
𝐿𝐿 4 𝐿𝐿 4 𝐿𝐿^4 𝐿𝐿^4
𝐿𝐿𝑒𝑒𝑒𝑒
UTD physics - Fall 2023
Take any rechargeable cells out of the battery-holders and put them in the charger. (Make sure that you get the polarity of the battery right.) If your group used any apparatus from another work-area, then please return it.
Ask your TA to check that your apparatus is back in-place before you turn in your reports. Please return wires to the wire-holder as in the photo in Electricity I.
The pre-lab for electricity IV is not short and you might like to begin it in this lab if
time allows. As always, begin the pre-lab early so that you are ready to ask questions
during office hours.
