April 9 Current and Resistance

We began the class with the discussion of current flow, and to gain a better understanding we conducted our first experiment. 

Lighting a Bulb

You can begin to explore circuits and currents by lighting a bulb with a battery.  You will need:

• 1 #14 V bulb

• 1 D-cell battery, 1.5 V, alkaline

• A piece of wire

Use the materials listed above to find some arrangements in which the bulb lights and some in which it does not light.  For instance, does the bulb light up in the following arrangement?

Activity:  Arrangements that Cause Light

a. Sketch two different arrangements in which the bulb lights

b. Sketch two arrangements in which the bulb doesn’t light.

Our Answesr to the questions above. We drew two scenario that would produce light and two that wouldn't.

 c. Examine the bulb closely.  Use a magnifying glass, if available.  The image shows the parts of the bulb that are hidden from view.  Why is the filament of the bulb connected in this way? 

The filament of a light bulb is connected directly to the conducting metal so that a charge can be produced thus creating energy and producing light. 

      d. Describe as fully as possible what conditions are needed if the bulb is to light and how these conditions are not satisfied in the arrangements that fail to cause the bulb to light.

In order for a light bulb to light there must be a closed circuit and electric flow must pass through the filament. In both scenarios that failed to produce light, there was no closed circuit and the electric current was not passing through the filament. With no electric flow there is no energy thus there is no heat to light up the bulb.

e.  Now use a second battery and connect it so that the bulb lights twice a bright as previously. 

part E

We were asked to make the light bulb as dim as possible with a specific arrangement.

We then continued class with our next demonstration of an electroscope. An electroscope is an early scientific instrument that is used to detect the presence and magnitude of electric charge on a body. Electroscopes detect electric charge by the motion of a test object due to the Coulomb electrostatic force.

Professor Mason began the experiment by rubbing the electroscope with wool to build up electrostatic (negative charge), the two plates inside the box then gain the same charge thus causing them to repel each other. He then touches the rod of the electroscope with the positive end of a battery and nothing happens, this is because there is no closed circuit for the current to flow through.

Next part of class we conduct the modeling of a simple electric circuit

Here we answered the question: why do you need a wire to go back from the bulb to the battery?

Our answer: So that the electrons can flow in and out of the battery causing an equilibrium charge.

Next activity we are given the following question: 

our answer was that we needed to  know the height of the waterfall and the rate of the current flow. What we found is that electric circuit is much like the flow of water. For example, a pump does work on the water to raise it to the top (pump gives Potential energy to the water). It maintains a difference in height between the two side. The water falls and gives up that stored PE to the waterwheel; meaning it produces work. In an electric circuit, the battery serves as a "pump" to pump the changes to the top of an electrical "cliff." The battery gives potential energy to each charge it raises up to the "top". When the charges "fall down" they give up their energy to the bulb, their PE is then transformed into light or heat.

Here we discussed the relationship between voltage(which determines how much potential energy the battery gives to each charge it raises up to the "top", current (measures how many charges flow through the bulb each second, and Power (measures the amount of energy delivered to and radiated by the bulb as heat and light every second.

We concluded that voltage is equal to power over current. We also did an example, which is pictured above.

Next activity we did was measuring current with an ammeter.

Our answer to this experiment was 46 milliamps, and we found a positive answer. What we found is that current doesn't change when energy changes. This is because there is an equal current going in as there is going out.

Current in a Wire

In our next activity we discuss what four things we need to know to find the current in the wire.

we said: charge of q, density, volume, and drift velocity.

Current is a measure of the rate at which charge is flowing past point in a wire.

Definition: Instantaneous Current

In this next example, we are introduced to drift velocity.  

Relationship between current and drift velocity:

When a Voltage is applied across the ends of a wire, an Electric Field is created inside the wire, E = V/L where L is the length of the wire.

In a vacuum the electric field would cause a charge to accelerate. In a wire, collisions of the conduction charges with impurities, imperfections, and vibrations of the atomic lattice causes the motion of the conduction charges to be slowed down. This represents a loss of energy which is dissipated as heat.

Over a wide range of conditions, the flow of the charges quickly achieves a steady state value and remains constant. The "average speed" at which the "free" charges are moving in the wire is called the drift velocity v_d.

The charge carriers in a wire are normally electrons. The number of conduction electrons "free" to participate in the current flow depends upon the atomic structure of material making up the wire. Conductors have many electrons that are able to participate, where as insulators have few free electron. Semiconductors are materials that lie somewhere between these two extremes. 

The current in a wire can be expressed as function of the number of charge carriers/volume, the magnitude of the charge carriers, the drift velocity of the charge carriers, and the cross-sectional are of the wire, 

Here we solved for drift velocity using the equation we derived in class for current.

Example: the 12-gauge copper wire in a home has a cross-sectional area of 3.31x10^-6 m² and carries a current of 10 A. The conduction electron density in copper is 8.49x10²⁸ electrons/m³. Calculate the drift speed of the electrons.

We continued class with the study of resistance and Ohms Law

We found that when a potential difference is applied to the ends of a wire, current begins to flow. However, the current is different for every type of material even if the voltage is the same. 

Resistors are used in a circuit to control the current flow or the voltage at different locations in a circuit. With this idea we moved onto our next experiment in which we measured the current and potential difference of a wire. The following graphs are the results of the experiment.

Here we have our prediction of what we thought the potential difference and current graphs would look like.  We made our linear which was obviously incorrect. Next to our predictions we have our derivation for potential difference.

Here we found that resistance is proportional to the length of the wire. If we increase the length of a wire or make its cross-sectional area smaller, the wire's resistance will increase.