April 14 Electric Potential

Purpose: Today we will continue our studies with electric potential energy and electric power. We will see how work is related to the two and also see how it is similar to the potential energy in kinematics. The difference now is that we are dealing with voltage and electric charges.



Dimmest and Brightest Light Bulb Experiment



We began the day with a light bulb experiment. We were asked to create circuit setups in which one would allow the light bulb to light at its brightest and the other set up would make the light bulb be at its dimmest.

Here we have our light bulb setup in series which made it light at its brightest. It is lighting at its brightest in series because  here the voltage is at its highest. If there is higher voltage this means that there is a higher potential energy and thus more work being done.

Next setup, we have our light bulb at its dimmest and in parallel. When we have a parallel circuit, the current is at its highest but it doesn't mean voltage is also at its highest, this is a perfect example of that concept.

Professor Mason then showed us how to properly draw circuits, for example, a light bulb, battery, etc. We drew a picture of our newly created circuits then re-drew them using the drawing techniques Mason showed us.

Water Heater Experiment

In this next experiment, we were shown how voltage affects the temperature of water.

We began we heating the water at a constant temperature for two minutes, then doubling the voltage for two minutes and graphing that.

This is our graph of the heated water before doubling the voltage

This is our graph of heating the water after doubling the voltage.

After conducting both scenarios, we clearly see that the slope became steep when the voltage was doubled. A steep slope indicates that there was a rise in temperature. However, we found that there was a change in temperature by a factor of 7 experimentally, we were told that this number is too high so we were asked to calculate this factor theoretically.
We used P=VI and V=IR

2V=2IR

P=2V2I

P=4VI
We then find a more accurate factor, which is 4.

Here a discussed what variables we needed to change the temperature of the water.

In our next activity(pictured below), we were asked to calculate work in an electric field under different circumstances.

Activity: Work done on a charge traveling in a uniform electric field
1.) A charge q travels a distance d from point A to point B;  the path is parallel to a uniform electric field of magnitude E. 
 The work would be mgh.

2.) The charge q travels a distance d from point A to point B in a uniform electric field of magnitude E, but this time the path is perpendicular to the field lines. 

The work would be potential energy.

3.)The charge q travels a distance d from point A to point B in a uniform electric field of magnitude E.  The path lies at a 45° angle to the field lines

The work done would be zero.

Here we were asked to rank work from most to least, as shown above. We found that A produced the most work which is given by the equation W=Eqd, then it was C which is W= Eqdcos(theta), and finally B which is W=0.

Next we derived the equation for electric potential energy, which is shown in the picture below. We found that electric potential energy is equal to the integral of the vector of the electric field multiplied by the vector  ds. We also derived the electric potential energy equation for a equal potential line, which says that electric potential energy is equal to Kq divided by r times vector ds.

In the last past of class, we were asked to conduct an electric potential field in Vpython. We were given the code and began to construct (picture below). 

We were then asked to calculate the electric potential of each point with respect to every corresponding observation point(pictured below). We were then asked to re-write the given program and also add an addition charge and corresponding observation point and then calculating the electric potential for each( pictured below).