14 - Passive RC & RL Circuit Natural Response

INTRO: Today we began we RC circuits. RC circuits, or first order circuits, include a capacitor, as well as a resistor. They are also called first order circuits, since the derivation of circuit element values involves first order differential equations.


Below is a diagram of a RC circuit. In this case you have an EMF (battery), capacitor, resistor, and a switch all connected in series. The capacitor will charge when it is in a completed circuit. When it is fully charged, the current can no longer flow as there is no potential difference between the EMF and the capacitor. If the capacitor is put into a completed circuit with a resistor and no EMF, it will discharge and temporarily power the circuit.

LAB: PASSIVE RC CIRCUIT NATURAL RESPONSE

In this lab we will examine the natural response of a simple RC circuit. We will use a time varying voltage source and switch. The natural response is the response of the capacitor on the circuit when the EMF is disregarded. Just to mention, the EMF response is called the forced response.

Below is a diagram of our circuit for the RC Circuit. In the pre-lab we calculated Tau (t), which is called the time constant. This value is Resistance/capacitance and is used as a marker on the capacitor discharging in the circuit. We calculated our time constant to be .015seconds, which is the discharge of the capacitor with no EMF connected in the series.

Below is a picture of the circuit we actually built. At first it may look different from the diagram above, but that is because we simply placed 3 capacitors in series to create an equal capacitance of what we wanted. We did this because we did not have the correct single capacitor in stock. 

 

Below is the voltage graph of the passive response of our RC circuit over 1 time constant. The graph is what to be expected of a normal discharging capacitor. Our experimental Tau was .020, which was off by a large percentage from our theoretical value.

LAB: PASSIVE RL CIRCUIT NATURAL RESPONSE

In this lab we will examine the natural response of a simple RL circuit. We will use a time varying voltage source and switch much like the above circuit.

Below is our circuit, with the inductor being the black cylinder in the center of the circuit. For an RL circuit, tau is inductance over resistance. Also, 5tau is when both an RC and an RL circuit are considered fully discharged.

We were short for time, so Professor Mason had to share the per-calculated results of the Lab.

13 - Capacitor Voltage -Current Relationship

INTRO: Today we began dealing with capacitors, which we have previously covered in our Physics class. Although we did the basics of capacitors in circuits, we will go much more in depth with this circuit element in this class.

Pictured below is a capacitor. Capacitor are circuit elements that store energy/voltage in the Electric Field between two plates within itself. When charged, a capacitor can directly power a circuit for a short time since it has stored voltage. This is temporary though, since the voltage will eventually balance itself out. Capacitors are measured in capacitance (C), which is essentially how much energy a capacitor can hold.

 

LAB: CAPACITOR VOLTAGE - CURRENT RELATIONSHIP

In this lab we we see what relation exist between the voltage difference across a capacitor and the current passing through it. From what we know from capacitors, the higher the current should slowly decay while the potential stored inside the capacitor increases.

Here is a picture of our circuit diagram with a resistor in series with a capacitor. We will use several time-varying signals to power our circuit.

 

The time-varying signals we used our displayed below. We will use the common sine function, as well as the more uncommon triangle function.

 

Below is a picture of our diagram. We have the voltage going in and out, as well as the resistor in series with our capacitor.

 Below are the aforementioned time-varying signals that were applied as the voltage. The first two graphs show sine functions at 1 & 2 KHZ, as well as a triangular function of 400HZ.

 

Viewing the graph below you can see the relationship between the voltage  and current. They are out of phase by practically 90 degrees. This experiment backs up what we already know about capacitors, that the current drops to 0, when the voltage reaches its' max.

*12 - Temperature Measurement Design

INTRO: Today we mainly dealt with a lab that incorporated familiar and unfamiliar components. We again use the thermistor, a device previously described, to create a relationship between temperature and circuit element values.


Pictured below is a thermistor. Since previously mentioned, the following description will be brief. This circuit element changes the current, and accompanying voltage, flowing through it based off of the temperature of the thermistor. For example, to change the current, holding the thermistor, would change the current through it since you are heating it up.


LAB: TEMPERATURE MEASUREMENT SYSTEM
In this lab we will design a DC circuit that will ultimately allow us the ability to determine the temperature. We will use a thermistor, a difference amplifier, as well as a Wheatstone Bridge Circuit.

Pictured below is the basic setup of our circuit. We will go from the thermistor to the Wheatstone Bridge to the Difference Amplifier


 Below is a diagram of our wheatstone bridge circuit. This circuit design is useful since wheatstone bridge circuits are often used to convert variations in resistance to voltage variations.


Here are our measured values for our setup


 Below is a picture of our circuit. As you can see on the right side of our circuit, we have placed a potentiometer. A Pot makes this circuit much easier to since it can be set to the correct resistance to meet our needs.


The next part of the circuit is to go through the OP AMP. We used a difference amplifier to measure the difference between the input and output voltage. Pictured below is the difference amplifier we built