Current and Resistance

Here we are trying to light a light bulb given two batteries, a conducting wire, and the light bulb.

In order to light the light bulb, a path needs to be created that would allow charge to flow through the batteries, through the bulb, and into the wire. If the wire is connected to both terminals, then simply touching the bulb to the wire will not light the bulb since charge is not flowing through the bulb.

The device above is called an electroscope and is used to observe the presence of charge. Rubbing a metal rob with animal fur, and then placing the rod in contact with the buld will cause the filaments to repel away from each other. This is an effect of the charge that was placed on the rod due the fur traveling down into the filaments. 

If we touch the positive end of the battery to the electroscope, nothing happens because there is no path for charge to move. Also, a closed circuit is needed in order to ensure a constant flow of charge. If there were no closed circuit, then eventually, a charge would build up, and repel any incoming charges, essentially stopping the flow of charge.

In order to analyze the amount of energy flowing into and out out a bulb, we connected a multimeter in series with a light build and battery. We predicted that less energy would leave the bulb than had originally entered. However, when we connected the multimeter in series after the current passed through the bulb, we see that it is the same current that had passed into the bulb. This means the current throughout a circuit in series in constant. Knowing the drift velocity of the charge carriers, the charge of the carriers, the number of charged particles for a given volume, and the cross sectional area allows you to find the current.

When comparing the current running through a wire to the potential of one end of the wire with respect to the other end, we see that they share a linear relationship. As the current running through the wire increases, the potential (voltage) also increases.

Solving for the drift velocity, we see the it is extremely small. As electrons move through the wire, they constantly crash into other particles, slowing their progress as they make their way across the wire.

A longer wire has more resistance than a shorter wire of the same material since their is more material. We see that the ratios of the resistances are the same as their ratio of their lengths. We can use this ratio to solve for unknown ratios and unknown lengths. Also, increasing the diameter of a wire creates less resistance. This is analogous to a water hose with a wide opening being able to push more water through relative a a water hose of smaller diameter.