Electric Circuits Worksheet 2 Charge Flow Model Answers For Essays
I and V
Electric current is the flow of electrically charged particles. In a metal free electrons are able to move independently. If the electrons in a metal move the same way, there is a net (overall) movement of charge. This is electric current. The atomic nuclei (lattice ions) in a metal are more or less locked in position, so the positive charges cannot move.
BUT
Just because the electrons are moving does not mean that the metal is negatively charged. Overall there are just as many positive and negative charges in the metal, so the metal is electrically neutral.
Electric current is the number of charges passing a point in a certain time. It is measured in AMPERES (Amps), A.
Current then is charge flowing per unit time.
I = dQ/ dt,
where I = current, Q = charge and t = time.
Question:
Recalling that the unit of charge is a Coulomb (C), and that an electron has a charge of 1.6 x 10^{-19}C.
How many electrons have to pass a point every second for 1A of current to flow?
Worked answer:
1A = 1 coulomb per second. 1 Coulomb must pass a point each second. So the question is how many electrons in 1C?
Number of electrons in 1C = 1C/ Charge on 1 electron
= 1C/ 1.6 x10^{-19} C
= 6.24 x 10^{18}
Conductors and Insulators
Basically the classification of materials into one of these two catagories depends on how free the charges are to move through the material under test.
In a conductor charges are free to move. In solids (metals), this means that the electrons are delocalised (not bound to any particular atom, and free to transfer between them). At any one moment, however, any electron is still associated with an atom, it's just that this atom changes with time.
In an insulator charges are not free to move. This means that electrons remain bound (localised) to a single atom, and cannot move from one to another, thus preventing the flow of charge (current).
How and why do electrons move?
This is because of a Potential Difference. Any two places with a difference in electrical potential have an Electric field between them, and what do charged particles do in an electrical field? MOVE!
Current flows from positive to negative. BUT electrons move toward a positive charge. Why is this? (Ref: Hutchings pp240)
An electric field is created in a wire by setting up a potential difference between different points along it. This electric field exerts an electric force on the free, charged electrons and causes them to move.
But the lattice ions have a large impact on the way the electrons move, causing collisions and the loss of electronic kinetic energy. Basically they slow the progress of the electrons to a crawl. The drift speed of electrons in a conducting wire is typically very low (mm/s).
BUT just because the electrons are moving slowly doesn't mean electricity is slow! In fact the opposite. The drift of electrons happens as soon as the electric field is applied, so there is instant current in all parts of the circuit. This is sometimes analogised to water in a pipe.
The amount of current in a wire can be calculated by considering the following steps...
1. Current is the amount of charge moving per second: I=Ne
2. The number of charges moving per second is the number of electrons per unit volume times the volume moving per second: N=nV
3. The volume moving per second is the cross sectional area of the wire times the drift velocity of the electrons: V = A v
So...
I = A v n e
Potential difference
Potential difference is the electrical energy transferred to other forms of energy per unit charge. It can also be called pd or voltage.
For example consider a resistor.
Charges move into a resistor with a certain amount of energy. The resistor tries to stop the charges, so they have to use up their energy to get through it. When the charges come out of the resistor they have less energy than they did to start with. The difference between the energy the charges started with and the energy they ended up with is the potential difference across the resistor.
For this reason we always connect a voltmeter in parallel .It measures the energy of charges as they go into a device, and compares it with the energy they have when they come out.
Another (possibly better) way of consifdering PD is interms of the electric field that causes charges to move and thus gives rise to electric current. We know from our work on Field theory, that charged particles in an electric field experience an electric force. We should consider this and it's implications for energy.
In an electric field, electric force acts on a charge. This force moves the charge, and does work on it. This work done means that the charge gains energy as it moves through the field.
The energy it gains will depend on the size of the charge, the electric field strength and the distance it has moved.
Energy = E x Q x d
If we combine E and d then we get a quantity called electric potential, V, which tell us how much energy a unit charge would potentially have if placed at that point in the field.
Energy = VQ
NB: Every point in a field has it's own value of potential, and points of equal potential can be linked to show lines of equipotential (see the drawing field patterns on conducting paper experiment).
The energy gained by a charge moving between two points at different potentials in a field is therefore given by the difference between its energies at those places in the field.
Energy gain = Energy_{1} - Energy_{2} = V_{1}Q - V_{2}Q
We consider the charge to stay the same, so...
Energy gain = (V_{1}-V_{2})Q,
And the quantity (V_{1}-V_{2}) is called the potential difference.
Thus we get the definition of the volt.
One volt is the electric potential difference between two places in a field which gives a 1 coulomb charge 1 joule of potential energy whe it moves between them. .
The electron volt
As you know a coulomb is a very large amount of charge. Similarly when we think about the typical types of particles affected by electric fields, a joule is a very large amount of energy. We define the electronvolt as a more convenient energy unit.
What do you think it is?
How big is it compared to a joule?
Question:
There is a potential difference across a conductor of 1.00 x 10^{4}V.
a) Find the work done by an electron of -1.6 x 10^{-19}C moving from one side of the conductor to the other.
b) Find the speed the electron leaves the conductor at assuming it doesn't collide with any other lattice ions in its path and it started at rest (m_{e}=9.1 x 10^{-31}kg)
The difference between PD and EMF
Voltages can be divided in to two types:
- Potential Difference (V) - This is when the charges lose energy as they move through an electrical component (eg: resistor, bulb, buzzer, etc).
- Electromotive Force (E) - This is when the charges gain energy as they move through an electrical component (eg: power pack, battery, etc).
Task:
Hutchings pp239-244, questions 14.1 - 14.8
Hutchings pp239-244, 249 , Kirk and Hodgson pp127, 130
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Resistance
Resistance
Resistance is technically the ratio between elexctrical pd and current. That's not practically much use to us, and we usually think of it as being a measure of how difficult electric current finds it to pass through a component.
Task:
Consider the implications on energy for the energy posessed/ transferred by charges moving around the following circuit. What is happening in each stage?
Ohm's Law:
States that for a metal conductor at constant temperature resistance is constant, and thus...
V a I
It is important to note that this is not alway the case, as the resistance of most devices changes with temperature. hence the more electric current passing through a device, the hotter it gets, and the higher its resistance tends to be.
Task:
Verify this theory, by drawing a VI graph for a filament lamp. What does the gradient of your graph represent?
Now carefully smash the glass bulb, taking care to keep the filament intact. Place the filament in a beaker of water, to keep it at a constant temperature, and repeat the experiment. What do you find?
Now explain your results interms of Ohm's Law.
Extension task :
What is a diode? What does its VI graph look like? How does it work?
Questions:
Hutchings pp247 qn 14.9-14.11
Important Note: When you draw a VI graph for a component, the gradient of the graph shows how the resistance of the compone t changes. To find the resistance at a particular point on the graph, you must do the calculation R = V/I for the values of V and I of the point you are interested in.
Hutchings pp244-247
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PSOW: Ohmic Behaviour
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Combinations of Resistors
Resistors in series
For a set of resistors in series:
1) The current flowing through all of the resistors is the same (current doesn't get used up)
2) The EMF across the power supply is equal to the sum of the Pd's across each resistor.
So given 3 resistors in series: R_{1}, R_{2}, R_{3}
The total Pd is the sum of the individual Pd's...
V_{T}= V_{1} + V_{2} + V_{3} | and V = IR, but I is the same in each case |
IR_{T} = IR_{1} + IR_{2} + IR_{3} | and cancelling for I gives |
R_{T} = R_{1}+ R_{2} + R_{3} |
Resistors in parallel
For a set of resistors in parallel:
1) The Pd flowing across each of the resistors is the same as the EMF of the power supply.
2) The sum of the currents going through the individual resistors is the same as the total flowing through the power supply
So given 3 resistors in series: R_{1}, R_{2}, R_{3}
The total current is the sum of the individual currents...
I_{T}= I _{1} + I _{2} + I _{3} | and I =V/R, but V is the same in each case |
V/R_{T} = V/R_{1} + V/R_{2} + V/R_{3} | and cancelling for V gives |
1/R_{T} = 1/R_{1}+ 1/R_{2} + 1/R_{3} |
Task:
PSOW: Resistors in Combination
Questions:
AS Level Resource Pack, p72
Hutchings pp267-269, Kirk and Hodgson pp131
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Resistivity
Resistivity, r, is a property of a material that allows us to calculate the resistance of a material of any dimension.
The formula relating resistance to resistivity is...
R= ρL/A.
Questions:
What do the values L and A represent?
How is this consistent with your understanding of factors that affect resistance of a wire?
Task:
Design an experiment to investigate the resistance of conductive putty.
Hutchings pp248, Kirk and Hodgson pp131
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Kirchoff's laws
Kirchoff's laws are a natural consequence of the principles of conservation of charge and energy.
They are principles that we have already used in solving circuit problems, and just require formal statementing.
Kirchoff's 1st Law
The sum of the currents flowing into any point in a circuit is equal to the sum of the currents flowing out of that point.
If you think about it this must be true, because charge can not be created or destroyed (conservation of charge), so unless it hangs around at the junction (which wouldn't make sense), whatever charge goes in must come out. Since current is the movement of charge this means that whatever goes into a junction, must come out again.
Kirchoff's 2nd Law
The sum of the EMFs around any loop in a circuit is equal to the sum of the PDs around the loop.
This is conservation of energy. If you think about voltage (EMF and PD) as energy per unit charge, then whatever energy is given to charge must be taken away. The EMF is giving charge energy and the PD is taking it away.
NB The only difficulty you might find with this law is choosing suitable loops to make a circuit problem easier to understand.
Questions:
Physics 1 pp113 - 118 : SAQs 14.1 - 14.7 and End of topic questions
Hutchings pp262-269
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Energy Loss in Circuits
Power loss
Recalling the equations for Potential Difference (and its meaning), and Current, we can derive an equation for lost in a circuit or component as follows...
DW/ Q = V and Q = I Dt to derive DW = I VDt
The rate of doing work is the power: P = DW / Dt = I V
Now check this is correct practically...
And with a joulemeter...
There are two other forms of P= V I, which you can derive by substituting with V= IR to eliminate V or I...
P = V^{2}/R = I^{2}R
Internal Resistance
So far in the electric circuits we have studied we have assumed that the components take energy away (Pd) and cells give energy (EMF). In actual fact the situation is a little more complex. Cells which supply energy to electrons also have a small amount of resistance called 'internal resistance'. This happens because in a cell, electrons have to travel through electrolyte, or wire, which have small resistances, while gaining the energy which the cell supplies.
To represent this we use a perfect cell and a resistor as one component.
We can work out what the internal resistance of a source of EMF is.
From Kirchoff's 2^{nd} Law we know that the sum of EMFs is equal to the sum of Pd's in a circuit.
We assume that no current flows through the voltmeter (this is a good simplification, because voltmeters have high resistance, and only a very small current will flow through it).
E = IR + Ir | and IR is measured by V |
E = V + Ir | rearranging this gives. |
V = E - Ir |
If we do an experiment with the above circuit to measure I and V for different values of EMF from the supply we should get a straight line graph.
- The equation for a straight line graph is y = mx + c.
- If we plot V against I, we can compare y = mx + c with V = -Ir + E.
- This means that the intercept on the straight line graph is E, and the gradient of the line is -r.
- Hence the internal resistance of the EMF source is found.
Question:
What is meant by the terms: 'terminal PD' and 'lost volts'?
Work through the worksheet on internal resistance and attempt Hutchings pp225 q14.14 to 14.17
Hutchings pp , Kirk and Hodgeson ppBack to topic 5
PSOW: EMF and Internal Resistance of a Cell
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The Potential Divider
We can use Kirchoff's second law to produce devices called potential dividers. These devices allow us to control the potential difference across a particular part of a circuit. This can be useful if we have components that require specific potential differences to operate.
We know that the total EMF in a circuit must be divided up between all the Pds of the components in the circuit.
If we have a supply EMF of 6V, and two resistors of 100W each in series, what is the Pd across each one?
If we have the same situation, but one of the resistors is 200W, what is the Pd across it?
By varying the resistances of the resistors in this way we can control the Pd across a particular point in the circuit.
How might we use this?
Task:
Use the croc clips program to investigate the affect of using different components in place of resistor R_{2}.
What sort of sensing circuits can you make in this way?
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Lesson Summary
Overview
Electricity -- we depend on it every minute of every day. And yet to many of us, electricity seems a mysterious and even magical force. Before Ben Franklin did his famous and very dangerous kite flying experiment, electricity was thought to be a type of fire. In 1847, the year Thomas Edison was born, most people considered electricity to be some sort of dangerous fad. By the time Edison died in 1931, entire cities were powered by electricity.
Although it has been used as an energy source for over 100 years, many people don't understand the basic principles of electricity. In this lesson, students begin to develop an understanding of electrical current. First, they act out an electric circuit. Then they use critical thinking skills and deductive reasoning to create their own electric circuits using a few simple materials. Next, students watch video segments of the ZOOM cast members using electric circuits to make a door alarm and a steadiness tester. Finally, students test the conductivity of a variety of materials.
Objectives
- Model the flow of electrons in a circuit
- Build an actual electric circuit
- Draw diagrams of electric circuits
- Explain how to tell when the path of an electric circuit is complete
- Test the conductivity of a variety of materials
Grade Level: 3-5, 6-8
Suggested Time
Multimedia Resources
Use these resources to create a simple assessment or video-based assignment with the Lesson Builder tool on PBS LearningMedia.
Materials
- balls, books, or erasers for the "Act Out an Electric Circuit" activity
- *wire strippers
- *insulated wire
- *flashlight bulbs
- *fresh D-cell batteries
- tape (masking or electrical)
- various materials for testing conductivity (suggestions: cardboard, salt water, aluminum foil, plastic, steel wool, wood, rubber, fabric, wire coat hanger)
*can be purchased at a hardware or electronics supply store
Before the Lesson
- Each pair of students will need two pieces of insulated wire, a battery, a flashlight bulb, and tape. Cut the insulated wire into six-inch segments. Remove one-half inch of plastic insulation off the ends of each segment. To do this, you can use wire strippers or you can score the plastic insulation around the wire with sharp scissors and then carefully but firmly pull it off with your fingers.
The Lesson
Part I: Act Out an Electric Circuit
1. Find out what students already know about electricity. Ask:
- What is electricity?
- What is electrical current?
- What is an electric circuit?
Have them draw examples of electricity and electric circuits in their lives.
2. Tell students that they cannot see electricity because electrons, the charged particles whose movement through a substance creates electricity, are too small to be seen even with a microscope. When electrons flow through certain substances (like copper wire), they form an electrical current. Electrical current provides energy to power all kinds of things, from video games to refrigerators to cars!
3. Act out an electric circuit, as follows: Ask students to join you in forming a circle. Tell students that you represent a battery and they represent a wire conductor. The circle represents a circuit. (Note: The word circuit comes from the Latin circuitus, which means "to go around.") Distribute an object -- like a ball, a book, or an eraser -- to each member of the circle, including yourself. Ideally, everyone should have the same object. Tell students that these objects represent electrons inside a wire conductor. Explain that a wire conductor is full of electrons.
Remind students that you are playing the part of the battery in this circuit, and explain that all batteries have a positive end, represented by your left hand, and a negative end, represented by your right hand. Pass your "electron" to the student on your right. The student receiving your electron should in turn pass the one he or she is holding to the right. Have students continue passing on electrons to the person to their right. Tell students that because electrons share the same negative charge, they repel one another, which keeps them moving along in the same direction. State again that the flow of electrons through a conductor is called electrical current.
4. Tell students that as long as the circle remains intact and the electrons continue to flow, their circuit is closed. To illustrate what happens when a circuit breaks, or opens, create a gap in the circle of students that is too wide across to pass electrons. The current will stop as a result.
Part II: Light a Bulb
5. Tell students that they are going to apply what they just learned about circuits to light a bulb. Divide the class into teams of two and distribute two lengths of wire (with the ends stripped), a flashlight bulb, a D-cell battery, and some tape to each team. Challenge students to use their critical thinking skills and trial and error to get their bulbs to light. Then have them draw a diagram of their circuit, making sure to include all its parts.
6. Have students report their findings. Ask:
- Did you get the bulb to light?
- In what order did you connect the parts?
- How did you know that electricity flowed?
- Can you trace the path of electrons in your circuit?
- What happened if the circuit was broken, that is, if there was a gap in the circuit?
7. Next, show students the following videos: Designing Electric Circuits: Door Alarm, Designing Electric Circuits: Steadiness Tester, and Experimenting with a Lemon Battery. Have students work in groups to diagram the circuit featured in one of the videos. Then have each group present their diagram to the class and explain how the electricity flowed through that particular circuit.
Part III: Explore Conductivity
8. Explain that substances through which electricity can travel easily are called conductors. Substances through which electricity has difficulty moving are called insulators. Then show students the Exploring Conductivity: Kid Circuits video. Ask them if the ZOOM cast members make good conductors. Tell students that the human body is not a very good conductor. Demonstrate by trying to light a bulb using your (dry) hand as part of the circuit. (The bulb does not light.) It is because of the remarkably low level of current needed by the digital clock in the video segment that the ZOOM kids' bodies are able to complete the circuit. Ask:
- Do you think the kids would be able to get a calculator to work?"
- What materials do you think might conduct electricity well?"
9. Challenge students to test the conductivity of a variety of materials, using the battery and bulb circuits they built in Part II. Have them begin by cutting one of the circuit wires in half and stripping the insulation off the two new ends. Then have students touch (or attach) both ends of the newly cut wire to various materials and record their results. (This is a great activity to do at home; students can simply carry the circuit with them from room to room, testing different objects.)
10. Ask students to create a class list of conductors and insulators on the board and categorize the objects by the materials they are made of: metal, glass, and so forth. Ask them to identify any patterns they see. Then introduce new materials to the list and ask students to predict whether each material is a conductor or an insulator. For example, if they found that tin foil and copper wire were good conductors, which do they think a paper clip would be?
Check for Understanding
Ask students to work in groups to act out a battery-bulb circuit and what happens when the light bulb burns out.
Related Resources to Check Out
- Lightning! QuickTime Video
This video explores the mysterious force of lightning. - Electric Girl QuickTime Video
ZOOM guest, Anna, loves electricity. Watch her construct a homemade flashlight.
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