Aquinas College Physics

Module 3.1.2: Sensing

Module 3.1.2

Sensing 3.1.2.C Circuit Laws 3.1.2.D Resistivity & Conductivity

Topic Notes Name:__________ -1-

Aquinas College Physics

Module 3.1.2: Sensing

Important resources for this module: All prezi presentations, booklets, homeworks and practical sheets are all available on the departmental website: http://www.aquinasphysics.com/312sensing1.html

https://www.alevelphysicsonline.com/electricity Excellent video tutorials made by an A level physics teacher for A level physics students. If you need to go over any concepts again, this is the first place that you should look. Free access to the course textbook (via the departmental website). Follow the instructions on the website for how to log in.

http://www.aquinasphysics.com/kerboodle.html Challenging questions from GCSE level to Undergraduate physics problems. If you are hoping for a B, A or A* you must be visiting this site and regularly practicing the problems. They also run excellent workshops. Look out for these!!

https://isaacphysics.org/

Multiple-choice practice revision questions on your phone. Revise on the bus on the way in to college!!

http://www.gojimo.com/ -2-

Aquinas College Physics

Module 3.1.2: Sensing

Series & Parallel Circuit Laws ......................................................................................................................... - 6 Series circuits .......................................................................................................................................................... - 6 A practise question on series circuits ................................................................................................................... - 7 Parallel circuits....................................................................................................................................................... - 8 A practise question on parallel circuits .............................................................................................................. - 10 Kirchoff’s Laws .................................................................................................................................................... - 11 Kirchoff’s first law ............................................................................................................................................. - 11 Kirchoff’s second law ........................................................................................................................................ - 11 Some example problems ...................................................................................................................................... - 12 A more complex problem .................................................................................................................................. - 14 -

Space for your own notes......................................................................................................................................... - 14 2.

Resistivity & Conductivity .............................................................................................................................. - 16 Key concepts ......................................................................................................................................................... - 16 Questions on resistivity and conductivity .......................................................................................................... - 18 Explaining resistivity/conductivity and the effect of temperature ......................................................................... - 20 Resistivity and logarithmic scales .......................................................................................................................... - 21 Finding resistivity & conductivity of a wire experimentally ................................................................................. - 22 -

3.

Isaac Physics Mastery Questions .................................................................................................................... - 23 Questions on Combinations of Resistors & Resistivity ......................................................................................... - 23 Questions on Kirchoff’s Laws ............................................................................................................................... - 25 -

Space for your own notes......................................................................................................................................... - 26 -

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Aquinas College Physics

Module 3.1.2: Sensing

Learning Objectives 3.1.2 (a) Describe and explain (vi) resistance and conductance, including series and parallel combinations (viii)

simple electrical behaviour of metals, semi-conductors and insulators in terms of the number density of mobile charge carriers

(x) Conservation of charge and energy (as represented by Kirchoffâ&#x20AC;&#x2122;s 1st and 2nd law) (b) Make appropriate use of: (i) the terms: series and parallel, resistivity, conductivity, charge carrier number density (c) Make calculations and estimates involving: (i) đ?&#x2018;&#x2026; = đ?&#x2018;&#x2030;â &#x201E;đ??ź ; đ??ş = đ??źâ &#x201E;đ?&#x2018;&#x2030;

(ii)

1â &#x201E; = 1â &#x201E; + 1â &#x201E; â&#x20AC;Ś ; đ?&#x2018;&#x2026; = đ?&#x2018;&#x2026; + đ?&#x2018;&#x2026; â&#x20AC;Ś (for series circuits) 1 2 đ??ş đ??ş1 đ??ş2 1â &#x201E; = 1â &#x201E; + 1â &#x201E; â&#x20AC;Ś ; đ??ş = đ??ş + đ??ş â&#x20AC;Ś (for parallel circuits) 1 2 đ?&#x2018;&#x2026; đ?&#x2018;&#x2026;1 đ?&#x2018;&#x2026;2

(iii) đ?&#x2018;&#x2026; = đ?&#x153;&#x152;đ??żâ &#x201E; ; đ??ş = đ?&#x153;&#x17D;đ??´â &#x201E;đ??ż đ??´ (d) Demonstrate and apply knowledge and understanding of the following practical activities (ii) determining the resistivity or conductivity of a metal

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Aquinas College Physics

Module 3.1.2: Sensing

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Aquinas College Physics

Module 3.1.2: Sensing

3.1.2 Electricity – Circuit laws, resistivity & conductivity These notes coordinate with the Prezi 3.1.2.C & 3.1.2.D on the departmental website & pages 46-55(ish) in the course textbook. Prezi 3.2.1.A Introduction to electricity https://goo.gl/11yLix

Prezi 3.2.1.D Resistivity & Conductivity https://goo.gl/97deHs

1. Series & Parallel Circuit Laws One of the most important skills that you will have to develop over this unit is the ability to design and build circuits with different components in them in order to do specific jobs – for example a circuit that can act as a temperature sensor or light sensor, a circuit with a particular resistance, a circuit whose resistance you can vary smoothly. In order to do this, it is vital that we understand how multiple components fit together in a circuit – specifically how we can calculate the combined resistance (and conductance) of a number of components combined in series and in parallel with each other.

Series circuits See the video at https://goo.gl/wnn1Ai (QR code right) for information on series circuit problems.

The simplest types of circuits to work with are series circuits, where resistors are placed one after another in a single complete loop.

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Aquinas College Physics

Module 3.1.2: Sensing

For the circuit shown, state the relationship between: (1) The total current leaving the power supply Itotal and the current I1 through resistor 1, the current I2 through resistor 2 and the current I3 through resistor 3.

Itotal =

(2) The total potential difference across the circuit Vtotal and the potential differences across each individual component (V1, V2 & V3)

Vtotal =

(3) The total resistance of the circuit Rtotal and the resistance of each individual component (R1, R2 & R3)

Rtotal =

(4) The total conductance Gtotal and the conductances of each of the individual components (G1, G2 & G3)

1â &#x201E; đ??şđ?&#x2018;Ąđ?&#x2018;&#x153;đ?&#x2018;Ąđ?&#x2018;&#x17D;đ?&#x2018;&#x2122; =

A practise question on series circuits For the circuit shown right, which is attached to a 12 V power supply, calculate: (1) The total resistance Rtotal

Rtotal =â&#x20AC;Śâ&#x20AC;Śâ&#x20AC;Śâ&#x20AC;Śâ&#x20AC;Śâ&#x20AC;Śâ&#x20AC;Ś ď &#x2014; (2) The total current flowing through the circuit Itotal

Itotal = â&#x20AC;Śâ&#x20AC;Śâ&#x20AC;Śâ&#x20AC;Śâ&#x20AC;Śâ&#x20AC;Ś A (3) The p.d across the individual resistors

V1 = â&#x20AC;Śâ&#x20AC;Śâ&#x20AC;Śâ&#x20AC;Śâ&#x20AC;Ś.. V

V2 = â&#x20AC;Śâ&#x20AC;Śâ&#x20AC;Śâ&#x20AC;Śâ&#x20AC;Ś.. V

V3 = â&#x20AC;Śâ&#x20AC;Śâ&#x20AC;Śâ&#x20AC;Śâ&#x20AC;Ś.. V

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Aquinas College Physics

Module 3.1.2: Sensing

Parallel circuits See the video at https://goo.gl/bRkweQ (QR code right) for information on parallel circuit problems.

More complex than series circuits are when components are placed in parallel across a power supply. Sometimes this can be because of the different ways in which parallel circuits are drawn. For example, the two circuit diagrams below show exactly the same circuit.

For the circuit shown, state the relationship between: (1) The total current leaving the power supply Itotal and the current I1 through resistor 1, the current I2 through resistor 2 and the current I3 through resistor 3.

(2) The total potential difference across the circuit Vtotal and the potential differences across each individual loop in the circuit (V1, V2 & V3)

(3) The total conductance of the circuit Gtotal and the resistance of each circuit loop (G1, G2 & G3)

(4) The total resistance Rtotal and the resistances of each of the circuit loop (R1, R2 & R3)

Itotal = Vtotal = Gtotal = 1â &#x201E; đ?&#x2018;&#x2026;đ?&#x2018;Ąđ?&#x2018;&#x153;đ?&#x2018;Ąđ?&#x2018;&#x17D;đ?&#x2018;&#x2122; = -8-

Aquinas College Physics

Module 3.1.2: Sensing

To fully understand parallel circuit laws, we need an appreciation of two things: the meaning of the term potential difference, and what the nature of what happens to the current flowing in a circuit when the resistance changes. Explain these concepts by answering the questions below. What is the definition of potential difference, V

Explain why this definition leads to the parallel circuit law relating the p.d. across each loop, as given on the previous page.

What happens to the total resistance of a circuit when another resistor is added to the circuit in parallel?

Explain why this happens.

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Aquinas College Physics

Module 3.1.2: Sensing

A practise question on parallel circuits For the circuit shown right, which is attached to a 12 V power supply, calculate: (1) (a) The total resistance Rtotal

Rtotal =…………………  (b) The total current flowing through the circuit Itotal

Itotal = ……………… A (c) The current through each individual resistor.

I1 = …………….. A

I2 = …………….. A

I3 = …………….. A

(2) For the circuit right, find the following: (a) The total resistance, Rtotal

(b) The current through the 40  resistor, I1.

(c) The current I2 through the resistor R2

(d) The resistance of resistor R2

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Aquinas College Physics

Module 3.1.2: Sensing

Kirchoff’s Laws For more information on Kirchoff’s laws see the videos linked to below: Kirchoff’s 1st law https://goo.gl/yiKpsz

Kirchoff’s 2nd law https://goo.gl/tq1xao

In understanding how to solve parallel circuit problems you immediately have an appreciation of Gustav Kirchoff’s (1824-1877) two circuit laws:

Kirchoff’s first law State Kirchoff’s first law in the space below:

What physical quantity is conserved in Kirchoff’s first law?

Kirchoff’s second law State Kirchoff’s second law in the space below:

What physical quantity is conserved in Kirchoff’s second law?

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Aquinas College Physics

Module 3.1.2: Sensing

Some example problems Some top tips and fool-proof methods for solving any circuit problem can be found with the video at https://goo.gl/LRuQY8 (QR code right). Top tip: If you are unsure of how to interpret a circuit diagram, then re-draw it in a manner that makes more sense to you. So long as all the parts of the circuit in series with each other remain in series, and all the parts in parallel with each other remain in parallel, this is perfectly valid and may help you answer questions on more complicated-looking circuits.

(1) For the circuits below find the: (a) total resistance; (b) total current flowing; (c) power of each resistor, and (d) p.d. across each resistor.

Circuit A:

Total resistance: …………..  

P150: …………… W

Total current: ……………. A

P110:…………. W

P.D.110:…………. V

P.D.110:………. V

Total current: ……………. A

P450:…………. W

P.D.450:…………. V

P.D.600:………. V

Circuit B:

Total resistance: …………..   P600: …………… W

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Aquinas College Physics

Module 3.1.2: Sensing

Circuit C:

Total resistance: …………..  

Total current: ……………. A

P300:…………. W

P500: …………… W

P100:……..…. W

P.D.300:………. V

P.D.500: ………… V

P.D100:……... V

(2) For the circuits below find the: (a) total resistance; and (b) p.d. across the power supply

Circuit A:

Total resistance: …………..  

Potential Difference: ……………. V

Potential Difference: ……………. V

Circuit B:

Total resistance: …………..  

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Aquinas College Physics

Module 3.1.2: Sensing

A more complex problem One more complicated question looks at finding the potential difference between two different point on a parallel circuit. Consider the question below: What is the reading on the voltmeter in the circuit right?

V = …………………. V Hint 1: what is the p.d. across the 100  resistor? Hint 2: what is the p.d. across the 20  resistor? Hint 3: what is difference between these values?

Space for your own notes …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. - 14 -

Aquinas College Physics

Module 3.1.2: Sensing

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Aquinas College Physics

Module 3.1.2: Sensing

2. Resistivity & Conductivity For more information on resistivity see the videos linked to at https://goo.gl/cbJ8jc (see QR code):

Key concepts When you looked at material science, one important distinction that we made was between properties describing the behaviour of a particular sample of material (force, extension, spring constant etc.) and the properties describing the behaviour of the bulk material (stress, strain, Young modulus etc.). Similarly, when considering the electrical properties of components and wires, we need to consider the difference between a sample of material and the bulk material itself. Consider the following examples of a piece of wire. (1) If a wire of length 1.2 m has a resistance of 2.0 , what is the resistance of a piece of the same wire which is 2.4 m long?

R = …………..  (2) If a 2 m long wire of cross-sectional area 1.0×10 m has a resistance of 3.0 , what is the resistance of a 2 m wire with a cross-sectional area of 2.0×10-6 m2? -6

2

R = …………..  (3) If a 4 m long wire of diameter 1.0 mm has a resistance of 0.64 , what is the resistance of a 4 m wire with a diameter of 2.0 mm?

R = …………..  (4) Using the model of electron flow through a metal wire (positive ions with a “sea” of delocalised electrons) explain your answers above.

electron

metal ions

Increasing wire length:

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Aquinas College Physics 

Module 3.1.2: Sensing

Increasing the cross-sectional area of the wire:

(5) In the boxes below state two relationships between: 2.

1.

The resistance R of the wire and its length L

The resistance R of the wire and its crosssectional area A

3.

The conductance G of the wire and its length L

4.

The conductance G of the wire and its crosssectional area A

We can combine statements 1 & 2 above to give a statement for the resistance R in terms of the wire’s length L and crosssectional area A. The proportional sign can then be replaced with a constant. This constant is known as the resistivity of the wire. State this equation in the box right.

State the units for resistivity, :

Similarly, we can combine statements 3 & 4 above to give a statement for the conductance G in terms of the wire’s length L and cross-sectional area A. The proportional sign can then be replaced with a constant. This constant is known as the conductivity of the wire. State this equation in the box right.

State the units for conductivity, :

R= Units:

G= Units:

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Aquinas College Physics

Module 3.1.2: Sensing

Questions on resistivity and conductivity (1) Complete the statements below: 

The resistivity of a material is equal to the resistance of a sample of that material which has a length of ……………… and a cross-sectional area of ………………

The conductivity of a material is equal to the conductance of a sample of that material which has a length of ……………… and a cross-sectional area of ………………

(2) The resistivity of copper is 1.7×10-8 m. Calculate the resistance between the ends of a 0.080 m copper rod which has a cross-sectional area of 3.0×10-4 m2.

R = …………….  (3) If a copper wire has a diameter of 0.500 mm, what length is needed to have a conductance of 2.75 S?

L = ………………… m (4) What is the resistivity of aluminium (at 20oC) if a 15 cm length of 2mm diameter wire has a resistance across its ends of 1.53 m?

 = ………..….  m (5) What is the cross-sectional area A of a 1.3 cm long carbon block shown, if its resistance is 2200  and the resistivity of carbon carbon is 3.5×10-5 m?

A

A = …………. m2 - 18 -

Aquinas College Physics

Module 3.1.2: Sensing

(6) This question is about a copper conducting bar which must carry a large current from a generator to a transformer in a power station. The bar loses 2 kW of power to the surroundings when it carries a current of 8000 A. Find the resistance of the bar and also its cross-sectional area, given that it has a length L of 10 m. The conductivity of copper is 5.9×107 S m-1.

R = …………….. 

A = ……………. m2

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Aquinas College Physics

Module 3.1.2: Sensing

Explaining resistivity/conductivity and the effect of temperature For more information on the effects of temperature on different types of materials (conductors and semi-conductors) see the videos at: resistance & temperature

semi-conductors

https://goo.gl/LUBSJG

https://goo.gl/4dVPVk

The resistivity/conductivity of a material is largely governed by the electron (or charge carrier) number density n of that material. Give a definition for this term and state its units: Electron number density, n

Units ………………. Complete the statement below: The greater the electron number density n of a material, the ………………… the material’s resitivity and the …………….. the material’s conductivity.

As well as the electron number density, another important factor affecting the resistivity or conductivity of a given material is the temperature T that it is at. In the box below, complete the sentences to explain how temperatures affect the resistivity of a metal wire.

In a metal wire, as temperature increases the resistivity  ……………………….

This is because higher temperatures cause greater …………………….. of the metal ions

Greater …………………… means that it is ……………………… for current to pass

Resistance (and resistivity) therefore ………………

If instead of considering a metal wire we investigate the effect of temperature change on a semi-conductor such as a thermistor, we find that another effect dominates. In the space below, explain what a semi-conductor is (you may wish to google it) A semi-conductor is…

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Aquinas College Physics

Module 3.1.2: Sensing

Complete the passage below to explain the effect of an increase in temperature on a semi-conductor such as the metal oxides used in thermistors:

In a metal wire, as temperature increases the resistivity  ……………………….

This is because at higher temperatures more ………………………… …………………….. become available cv

This means that greater …………………… can flow for a given potential difference.

Resistance (and resistivity) therefore ………………….

Resistivity and logarithmic scales Different materials have vastly different number of mobile charge carriers available to them – in other words hugely different values for the electron number density n. Therefore, when comparing the resistivity and conductivity of different materials we often use logarithmic scales (see below).

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Aquinas College Physics

Module 3.1.2: Sensing

Finding resistivity & conductivity of a wire experimentally You will be expected to be able to describe an experiment that you have undertaken to find the resistivity of a metal from which a wire is made. More details on this experiment can be found on the video at https://goo.gl/HLVVft (see QR code right).

For the experiment: (1) Describe the equipment that you used and the measurements that you took (include a labelled diagram)

(2) Explain how you minimised any experimental uncertainty and accounted for systematic error in your experiment.

(3) Sketch the graph that you plotted and how you used it to find values for conductivity and resistivity of the metal the wire was made from.

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Aquinas College Physics

Module 3.1.2: Sensing

3. Isaac Physics Mastery Questions These questions have their background in the ethos that anything is hard when you don’t spend much time on it, and that things become much easier the more your practice. You will know this if you are learning to drive, or when you pick up any other new skill for the first time. I would say that playing the piano is really really hard. But I’ve probably not spent more than a few hours when I was very young trying. Someone who has spent hours practising playing the piano would probably tell you that it is easy as it comes naturally to them – neglecting to mention all the hours of practice that they have put in.

PHYSICS IS NO DIFFERENT!! THE MORE YOU PRACTICE THE BETTER YOU GET.

Have a go at the mastery questions on the following pages. You can input your answers and check they are right on the isaacphysics.org website (see separate links for each section). You should be aiming to get correct at least the number given at the top of each section before you can consider yourself to have mastered each of these core concepts.

Questions on Combinations of Resistors & Resistivity *Starts easy, and gets harder – aim for 9/12 at least to gain a mastery of these concepts. These questions come from the Isaac Physics skills mastery book (buy this and the CGP revision guide through ParentPay for just £10!!). You can enter your answers and complete these questions with the Isaac Physics board at https://isaacphysics.org/s/knAJfX

. For these questions you will need to refer to the circuits below

(1)

What is the resistance of circuit combination A?

(2)

What is the resistance of circuit combination B? - 23 -

Aquinas College Physics

Module 3.1.2: Sensing

(3)

What is the resistance of circuit combination C?

(4)

What is the resistance of circuit combination D?

(5)

What is the resistance of circuit combination E?

(6)

What is the resistance of circuit combination F?

(7)

Complete the table below linking the electrical and dimensional properties of different wires. Resistivity / m

…………………

Wire thickness cross-sectional area is 2.1×10-6 m2 cross-sectional area is 0.50×10-6 m2

1.0

4.9×10-7

15000

1.0 cm diameter

1.5×10-7

Length / m 68

1.5×10-8 4.9×10-7

Resistance /  ………………….. 15 …………………. …………………

(8)

Conventional domestic 13 A sockets are connected with copper cables with a cross-sectional area of 2.5 mm2. Copper has a resistivity of 1.5×10-8 m. What is the resistance of 20 m of cable?

(9)

A high voltage wire for transmission of electricity across the country is made of 10 aluminium wires (resistivity = 2.5×10-8 m) wound together with 15 copper wires (resistivity = 1.5×10-8 m). If all the wires have a radius of 2.0 mm, calculate the overall resistance of 20 km of cable (the aluminium is there to give strength to the cable).

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Aquinas College Physics

Module 3.1.2: Sensing

Questions on Kirchoff’s Laws *Starts easy, and gets harder – aim for 13/17 at least to gain a mastery of these concepts. These questions come from the Isaac Physics skills mastery book (buy this and the CGP revision guide through ParentPay for just £10!!). You can enter your answers and complete these questions with the IsaacPhysics board at https://isaacphysics.org/s/gt46ax. You will need to refer to the circuits below:

In the table below fill in the currents and voltages to complete the gaps. Label

Current / A

Voltage / V

Label

Current / A

Voltage / V

(A)

…………….

2.0

(H)

…………….

9.0

(B)

…………….

…………….

(I)

…………….

…………….

(C)

…………….

…………….

(J)

…………….

9.0

(D)

0.20

…………….

(K)

3.0

…………….

(E)

…………….

…………….

(L)

…………….

2.0

(F)

0.20

…………….

(M)

2.0

…………….

(G)

…………….

3.0

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Aquinas College Physics

Module 3.1.2: Sensing

Space for your own notes …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………………………………………………………………………………..

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Aquinas College Physics

Module 3.1.2: Sensing

…………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………………………………………………………………………………..

- 27 -

Aquinas College Physics

Module 3.1.2: Sensing

…………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………………………………………………………………………………..

- 28 -

Aquinas College Physics

Module 3.1.2: Sensing

…………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………………………………………………………………………………..

- 29 -

Aquinas College Physics

Module 3.1.2: Sensing

…………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………………………………………………………………………………..

- 30 -

Aquinas College Physics

Module 3.1.2: Sensing

- 31 -

3.1.2.C&D Circuit laws & resistivity
3.1.2.C&D Circuit laws & resistivity