23-Feb-2016: Day 1

Exercise 1:

Warming up with an exercise.

Problem:

     "The charge transferred in time is given as shown below where the peak value is 10 C and the           time at the maxima is 0.785s.  Determine the current, I(t), flowing through the wire."

Solution:

Problem:

     "Determine the total charge flowing through an element for 0 < t < 2  seconds when the

        current entering its positive terminal is i(t) = e^(-2t)."

Solution:

Problem:

     "Given v = 10V and i(t) as shown below, sketch the power and energy as a function of time."

Solution:

     Our attempt at sketching this using P = VI.

     

     A separate group confirmed our findings.     

Exercise 2: (Lab)

Learning the fundamentals of a solderless breadboards, open-circuits, and short circuits.

Lab P. 1:

     Using the digital multimeter (DMM) we connected the leads to two spots along the same row and

     measured a value for resistance, meaning that these nodes operate as a closed circuit. 

     R = 1.8 Ohms

Lab P. 2:

     Using the same setup from P. 1, we found that every row on the breadboard is split down the

     middle. We did so by connecting the leads of the DMM across the center divider along the same

     row and noted that there was no reading in the DMM meaning that the circuit was not closed. 

     R = 0 Ohms

Lab P. 3:

     Now connecting two arbitrary nodes of different rows it was also concluded that columns are not

     connected in any way, an open circuit.

     R = 0 Ohms

Lab P. 4:

     Leaving the setup from P. 3, we bridged the two rows belonging to each column and found that

     this closed, completed, the circuit. 

     R = 4.5 Ohms

     Post lab, including clean up, we were asked to recall what the solderless breadboard looked like
     and how the elements were connected. Below, is a sketch where the green dots represent the ports
     and the red lines show the relation between the rows and most outer columns.

     Components can only be connected in series if one of their terminals is connected to the same row
     as another component's terminal and so forth. The ends of the series may then be closed by
     connecting them to the outer most columns which are common energy and ground sources.

Exercise 3:

Problem:
     "The figure shows the current through and voltage across a device.  Find the total energy
        absorbed by the device for the period 0 < t < 4 seconds."

Solution:

     At the top of the whiteboards we drew the given current and voltage versus time graphs. From
     theses graphs we were able to sketch a "good enough" representation of the power versus time
     graph to then be able to project and sketch the energy as a function of time graph.

     Using the power graph, equations for both current and voltage may be derived.

P = 250t^2, 0<t<1

P = 250t, 1<t<2

     By adding the two and integrating them with their respective boundaries, the total energy can be

     calculated.

Exercise 4:

Problem:
     "Given the circuit below, find V₀.  Hint:  Be sure to use conservation of energy or that the sum
       of the power in all the elements is 0."

Solution:
     In any loop, the sum of the voltages is zero. Also, a current splits proportionally to the resistances,
     or in this case the voltages, of the elements which is how the mystery voltage, V1, was calculated.