2/25 Circuit Analysis and Breadboards

We are introduced to the idea of branches, nodes, and loops and were asked to identify how many of each were in the given circuit.

We are given a circuit analysis problem and asked to find the multiple ways the problem can be solved, because there are 3 currents and the first current must be positive, we have 4 total possibilities. We found the current for each of the 4 combinations.

We are given another circuit analysis problem where we have a circuit and we are asked what will happen to two light bulbs in the middle of the circuit once the switch closed. Because the voltage potential difference at the points above and below each light bulb was always 1V, we found that the light bulb did not get brighter or dimmer.

We did a lab with the breadboards again except this time we used a special device that allowed us to control the voltage that we send through the breadboard.

We manually adjusted the voltage from 0 to 2 with .2 increments for the voltage so that we could test for the current going through the circuit as well. We also read the voltage with a multi-meter to see what the experimental voltage is. We found the resistance going through our advertised 100 ohm resistor to have an actual resistance of 98.3 ohms from the data collected. 

We graphed the data we produced from our lab and plotted it on a graph. Once we plotted it, we found the relationship between current and voltage to be linear and our r-squared value to be greater than .98 (which in statistic terms indicates that it fits a linear curve very closely). 

We are given power, voltage, and resistance and are asked to find when the resistance is cold (when voltage is initially applied) vs when the resistance is hot (when the circuit has been running for a while). We found that the resistance of the resistor to be 192 ohms in the beginning and less than 192 ohms after.

We do another lab with the breadboards except this time we introduce something called  MOSFET to the circuit. The purpose of the MOSFET is to keep the voltage at a consistent level. The voltage is drained and applied to the circuit to maintain consistency. We found that the current this time around produced a graph much closer to a linear relationship due to the increased consistency provided by the MOSFET.

We set up another lab with the breadboards and multimeter to measure more data except this time we are using a MOSFET.

This is a graph of the along with the table of the data we collected from the lab with the MOSFET.

2/23 Relationship between Current, Power, Voltage, and Energy(Work).

We were given a problem in class where we were given the graph of charge vs time with the time and q max given and we were asked to create and solve the sinusoidal function of q with respect to t. Since we are given the maximum, we can say that the derivative of the derived equation is equal to the 0 when t is equal to when q is at a maximum.

With the same problem, we created a function of current in terms of time. We used the derived current equation to find the total charge between 0 and 2 seconds.

In this problem, we are given the current vs time graph and the voltage is 10V. We were asked to create the power vs time graph and work vs time graph. Because P = VI, We can multiply 10V to every point on the current vs time graph which is why the power vs time graph is so similar to it because only the scale of the y axis changed. We then did the same thing to find the work vs time graph by saying dw/dt is equal to power. We used the properties of a derivative to draw the work vs time graph. We were then asked to calculate the total work done between 0 to 4 seconds. 

In this lab, we used a breadboard to find the resistance of a row in the breadboard. (Randomly chosen row). We found the resistance to be 1.4 ohms.

Using the same breadboard, we found the resistance of row 22. The breadboard does not have a complete circuit if the circuit extends across the entire row. A complete circuit can only be created if it is in the same column. This is why when we tested the entire row of 22, we found the resistance to be infinity or overload because if the circuit isn't complete, the resistance is infinity. When we tried row 22 in the first column and row 34 in the second column, we also could not create a complete circuit hence the infinite resistance.

This is the breadboard mapped out with what is connected to what.

We are given the problem of trying to derive other graphs given the current vs time graph on the top left corner and the voltage vs time graph on the top right corner. Because of the formula P = VI, we can simply multiply the values of both graphs at the same time and find the power for that same time. The power graph we came out with is on the bottom left. We then found the energy vs time graph by saying that the integral of Power with respect to time is equal to work. We used the properties integration to predict what the graph will come out to be. 

Now that we found the power and energy vs time graphs, we are asked to calculate the total work done between 0 and 4 seconds. We integrate power with respect to time between 0 and 4. Since we do not have an equation for the graph, we found the area under the curve algebraically. The curve between 0 and 1 is not linear so we created an equation for that specific part of the graph to find the area underneath 0 and 1. 

We are given a circuit analysis problem where we are asked to find the power absorbed and each resistor using Kirchoff's Voltage Law and we also calculated the power delivered into the circuit.