Electronics:

Below is an electron gun with vertical and horizontal deflection plates.

Below is an oscilloscope. In an oscilloscope, the horizontal deflection plates move the spot horizontally across the screen. This represents time. The vertical deflection plates represent voltage.

 

The intensity knob on the oscilloscope either increases or decreases the voltage and makes the image brighter. When an increased voltage is applied, the amplitude of voltage changes. The other controls and functions are displayed below. 

The relationship between Volts/Div and the vertical deflection of the spot are described.

We connected a battery in series with a tap switch to the CH1 input plug. We tapped the key and observed how the change in voltage causes the amplitude to move up and down.

This graph on the oscilloscope is a measure of voltage in the battery we used. The original image was a straight line across the screen, but we altered the tim/div and were able to view the single horizontal line.

        Here are derivations for the acceleration and velocity of the electron moving between the two plates. 

Kinematics are used as well.

Next, we set our function generator at 96Hz and used the oscilloscope to determine the period of the sinusoidal wave form.  We then calculated the period and compared it to our experimental value gather from the oscilloscope graph. 

Here is an example of a square wave output when switch to AC mode. The set of two lines moves fast and at different amplitudes. The time base control can change the frequency of the graph.  

Below we recorded the characteristics of a transformer on a small DC wallwart connected to the oscilloscope. We then compared the visual output of the grey power supplies used previously. When set to AC, we were able to see all of the noise, and when set to DC, we got a clear reading of the actual voltage. AC transformers have an alternating signal.

The next 3 images are of the oscilloscope displaying different waves from being connected to 2 different function generators at different frequencies.

Summary: 

• An oscilloscope is a lab instrument used to produce visual displays of time varying voltages. 
• In an oscilloscope, the horizontal deflection plates move the spot horizontally across the screen. This represents time. 
• The vertical deflection plates represent voltage.
• The intensity knob on the oscilloscope either increases or decreases the voltage and makes the image brighter. 
• When an increased voltage is applied, the amplitude of voltage changes. 
• Using an oscilloscope, we can set the function generator to display a sinusoidal wave and determine the period of the voltage vs time. 
• Deflection of an electron passing between charged metal plates is proportional to the voltage across the plates. 
• We can use kinematics as well as the equation: F=qV to find the acceleration of a charged particle moving between the plates.

Capacitance & Decay

This image shows how we were to solve for current, voltage, resistance and power on our quiz. We used the looping method, Kirchhoff's Laws, and formulas for voltage and power.

A capacitor is a device that stores electric charge and electrical potential energy.

Capacitance is the measure of the ability of a device to store charge per unit of voltage applied across the device. It is a measure of the net charge per unit voltage.

The formula for capacitance between two charged plates is derived below.

Here is picture of a capacitor we used.

The formulas for capacitance in series and parallel circuits is as shown. We used the multimeter to find the capacitance of each capacitor.

In this problem, we solved for the total capacitance in a parallel circuit. The formula is similar to that of resistances in a parallel circuit.

Here we solved another capacitance problem. We also solved for the energy stored inside of the capacitor and its charge.

Capacitance of capacitors in series can be solved using the following formulas.

Capacitance of capacitors in parallel can be solved using the following formulas.

Similar to reducing resistances, we can reduce capacitance using the following method:

Formulas for finding voltage, current, resistance, capacitance, and charge in series and parallel circuits are shown below. 

In the next activity, we measured the change in capacitance at different separation distances. We placed two pieces of foil in different sections of our lab book and measured the capacitance using a multimeter.

From these measurements, we made the following calculations and graphs of capacitance vs separation distances.

The graph was displayed on logger pro and fit equation was found. As the separation distance increase, the capacitance decreases.

Here we used the capacitance formula and the separation distance to solve for the area of the capacitor's plates.

Below is a graph of current vs time for a discharging capacitor. The voltage, charge, and current of a discharging capacitor can be found using the formulas below. 

A capacitor charging will have an increase in current over time lapsed. when the current decreases, the charge decreases. The formulas below can be used to solve for charge on a capacitor as well as the current and voltage.

Below is a description of how a light bulb will react when it is connected to a capacitor in series with applied voltage. There is also a description of how a light bulb will react when there is no battery connected and only a capacitor.

The derivation for the theoretical decay curve is shown below.

In the RC circuit problem below, we solved for the time constant and time required for the capacitor to discharge to one electron.

Summary:

• A capacitor is a device that stores electric charge and electrical potential energy.
• Capacitance is the measure of the ability of a device to store charge per unit of voltage applied across the device. 
• It is a measure of the net charge per unit voltage.
• A capacitor charging will have an increase in current over time lapsed. when the current decreases, the charge decreases. 
• We can simplify capacitance in a circuit problem similarly to that of resistance. 

DC Circuits

Prof Mason provided an example of a DC circuit board. When the switch is turned on the lower bulb and upper bulb stay the same. The components are in parallel with one another.

This is a schematic of the DC circuit board.

Bulbs and batteries in relation to components being in series or parallel to each other:

In a series circuit, the voltage is additive.

Current in a parallel circuit is additive.

Below we used the given diagram to find the total resistance. The formulas for resistances in series and parallel is shown in red below. We first had to simplify the schematic. We found the resistance of box one and three. Then we solved for resistance of box two by using the simplified resistances from box one and three. 

When measuring voltage, we must always measure across an element. The voltage of the source is proportional to the voltage of the bulbs. The voltage in a series circuit is additive.

For current, we measure through an element. The voltage and current are proportional to one another. The current in a series circuit is the same at all points.

In parallel circuits, the voltage is the same at each point.

In parallel circuits, the current is additive.

 Here is a resistor connected in series.

Next, we used the following chart to compare our measurements of 4 resistors to accepted values.

The accepted values are on the left and the measured values are on the right. We used a multimeter and took down values for resistance. Each of the resistors had colored bands on them which allowed us to compared them to the chart above. All of our measurements fall within the accepted resistances.  

Summary:

• In series circuits:
• voltage is additive
• current is the same throughout the circuit
• resistance is additive
• In parallel circuits:
• voltage is the same throughout the circuit
• current is additive
• resistance is found using the formula: 1/Re=(1/R1) + (1/R2) +...(1/Rn)
• We can simplify schematics to solve for total resistance in a circuit when using the rules above.
• When measuring voltage, we must always measure across an element.
• For current, we measure through an element. The voltage and current are proportional to one another. 
• Resistors used in this lab were all marked by bands indicating the accepted resistances with uncertainty.