1. Current and Resistance

2. Goal of the class
Describe the basic properties of electric current, and solve problems relating current, charge, and time.
Calculate resistance, current, and potential difference by using the definition of resistance
Question of the Day: What factors affect the resistance of a piece of wire?
Previous answer: No previous question 
Previous question: What is the value of the electric field inside a conductor?

3. Question
The term resistance is often used when describing components of electric circuits.
What behavior of the components does this term describe?
Do conductors have resistance?
If so, are all conductors the same? Explain.
What effect would increasing or decreasing the resistance in a circuit have on the circuit?
You may wish to build a simple circuit with a battery or two, a bulb, and a switch with connecting wires. You could use this circuit as a focal point for the discussion of resistance. Ask students to think about what resistance might mean and how it would apply to the different components they see (bulb, wire, insulator on the wire, switch, and so on).

4. Electric Current
Electric current (I) is rate at which charges flow through an area.
SI unit: coulombs/second (C/s) or amperes (A)
1 A = 6.25  1018 electrons/second
Electrons are repelled from the negative terminal. As a result, they have high PE and flow toward the neutral plate. Eventually, as electrons build up on the plate, the PE of electrons on the plate equals that of the battery, and the flow stops. Similarly, electrons flow from the neutral right plate to a lower PE, the + terminal of the battery. Another explanation is that repulsion builds up between electrons on the left and right plates. This repulsion drives the electrons on the right plate to the battery terminal. + -

5. Conventional Current
Conventional current (I) is defined as the flow of positive charge.
The flow of negative charge as shown would be equivalent to an equal amount of positive charge in the opposite direction.
In conducting wires, I is opposite the direction of electron flow.
Capacitance is the ability of a conductor to store electrical energy by separating charges.

6. Velocity of Electrons Through Wires
When you turn on a wall switch for a light, electrons flow through the bulb. Which speed below do you believe most closely approximates that of the electrons?
The speed of light ( m/s)
1 000 m/s
10 m/s
m/s
Why do you think so?
Students may believe that the electrons must travel at high speeds to get from the switch to the bulb. You might ask them if the wire is already “filled” with electrons or if the electrons lighting the bulb are those that are “waiting” at the switch for it to close.

7. Drift Velocity Electrons undergo collisions with atoms in the metal.
They “drift” through the wire.
Drift velocity for a copper wire with a current of 10 A is m/s.
The E field moves through the wire near the speed of light, causing all electrons in the wire to move nearly instantly.
The electrons in a light bulb begin moving as soon as they experience the force of the electric field.

8. Resistance to Current Resistance is opposition to the flow of charge.
SI unit: volts/ampere (V/A) or ohms ()
Ohm’s Law : V = IR
Valid only for certain materials whose resistance is constant over a wide range of potential differences
This comes from Q=CV

9. Practice Problems
A typical 100 W light bulb has a current of A. How much charge flows through the bulb filament in 1.0 h? How many electrons would flow through in the same time period?
Answers: 3.0  103 C, 1.9  1022 electrons
This same 100 watt bulb is connected across a 120 V potential difference. Find the resistance of the bulb.
Answer: 1.4  102 
For problems, it is a good idea to go through the steps on the overhead projector or board so students can see the process instead of just seeing the solution. Allow students some time to work on problems and then show them the proper solutions. Do not rush through the solutions. Discuss the importance of units at every step. Problem solving is a developed skill and good examples are very helpful.
Q = Current x time = 0.83 C/s x (3600 s) = 2988 C = 3.0 x 103 C
(3.0 x 103 C) x (6.25 x 1018 electrons/C) = 1.9 x 1022 electrons
R = V/I = 120 V / 0.83 A =  = 1.4 x 102 

10. Resistance of a Wire
On the next slide, predict the change necessary to increase the resistance of a piece of wire with respect to:
Length of wire
Cross sectional area or thickness of the wire
Type of wire
Temperature of the wire
For problems, it is a good idea to go through the steps on the overhead projector or board so students can see the process instead of just seeing the solution. Allow students some time to work on problems and then show them the proper solutions. Do not rush through the solutions. Discuss the importance of units at every step. Problem solving is a developed skill and good examples are very helpful.
Students do not need to use Coulomb’s law to calculate the answer to the second question. Felectric = Eq0 is much simpler.
6.62  10-6 C or 6.62 C
1.19 N for both test charge and object

11. Resistance of a Wire
Ask students which types of wire has the least resistance.
Silver has the least resistance. Copper, gold and aluminum also have low values for resistivity.

12. Applications Resistors in a circuit can change the current.
Variable resistors (potentiometers) are used in dimmer switches and volume controls.
Resistors on circuit boards control the current to components.
The human body’s resistance ranges from 500,000  (dry) to 100  (soaked with salt water).
Currents under 0.01 A cause tingling.
Currents greater than 0.15 A disrupt the heart’s electrical activity.
The equivalent equations for PEelectric are:
PEelectric = 1/2C(V)2
PEelectric = Q2/2C

13. Question
The term resistance is often used when describing components of electric circuits.
What behavior of the components does this term describe?
Do conductors have resistance?
If so, are all conductors the same? Explain.
What effect would increasing or decreasing the resistance in a circuit have on the circuit?
Resistance is opposition to the flow of charge.
Conducting wires do have a very small resistance. This would be a good time to review how the resistance of wires depends on length, thickness, temperature, and type of wire.
Non-conductors have much greater resistance to the flow of electrons.
Adding resistance to a circuit will decrease the flow of current. Resistance is used to control the flow of current.

14. Homework
Please complete questions on page 616
Q 22, 29, 33, 35, 42