Alternating current L-R-C

inductance

Faradays law

Biot Savart

We begin with having a coil, a compass, and voltage source to explore the magnetic field produced by coils and its variance due to different currents. We derived an equation for the biot-savart law and used that to find an a equivalent for coils B(coil)=ulN/2R=B(earth)tan(theta)

We checked the currents with our ammeter in series in our circuit, again we used a potential source to observe the deflection of the compass needle for increasing currents.

We found the value of the magnetic field of the earth to 2.83*10^-5 T which accounted for by lining our compass up initially in the magnetic field so we could get good results from the magnetic field in the center of the coil that caused the needle deflection in our excel results and graph.

Motors

During this lab we experimented with an electric motor that utilized copper coils, magnetic fields, and current to cause torque on axle of the motor. The motor rotates 180 before  becoming an open circuit and letting the inertia of the armature close the circuit again and thus creating a torque.

We were tasked with creating our own motors using the ideas of coils, commutator's, and current. Next, we wrapped coils of copper for current to go through, sanded one end completely off and the other only partially to act as our commutator, then used a 3V source for our current.

This was our set up for our motor

 

 

 

 

We explored how  lines of current magnetic fields interacted. We found that they could be calculated using the principle of superposition, meaning equal and opposite currents magnetic fields would cancel out, while equal and same direction would be additive.

Magnetic Flux and Forces

During this lab we conducted experiments with magnetism, mainly focusing on magnetic flux and magnetic forces. We initially did a quick experiment with a bar magnet and compass, we used the compass tip as direction vectors that we plotted

 

Using metallic shavings we observed magnetic field lines similar to electric field lines but they are continuous. Sum B*da=0 gausses law for magnetic fields says that there are as many field lines coming in as leaving. They leave the north pole of the magnet bar and enter into the south pole. They have yet to observed as a monopole. 

 

 

Here we had a magnetic field produced by a permanent magnet with a current moving from right to left using the right hand rule. We expected to see a force move the copper pipe in our observation direction, which it did, thus confirming the formula for force in a magnetic field F=qv*B.

 

 

 

Here with our given information and the fact that  the pole had translational and rotational motion we had to utilize kinematics and the equation we found earlier in the day to find the value of the magnetic field 2.5 *10^-3 Telsa.

 

 

Next, we derived a proportionality between the magnetic field and the current present in the conductor.

 

Here we looked at torque and what factors contributed to a magnetic field causing moments. Using a rectangular square derived a relationship I that expressed torque as IAxB where we cross the factor Mu= IA with the mabgneticfield B.

Diode

During this lab we were introduced to diodes and transistors, the diode essentially allows current to pass through in one direction while blocking any current from entering from the opposite direction, the transistor can be utilized as a switch or even an amplifier, which is what we used it in for our circuit.

 

Using the breadboard we constructed the circuit that we were given in a diagram consisting of resistors, capacitors, diodes, and transistors .

 

 

 

We used that circuit as well as a phone and speaker to amplify the sound from the phone. We observed the two differing waves from the transistor and diode and the wave function generator.

 

 

Electronics

 

In this lab we used both a wave function generator and a oscilloscope to produce voltage's that vary over time and are displayed on the oscilloscope screen. The oscilloscope uses an electron gun to shoot electrons through two separate sets of deflection plates, the horizontal plates moves the electrons across the screen at a constant rate, The vertical plates receive voltage from input that is reflected on the screen, in this case the wave function generator.

 

The wave function generator is used to adjust  frequency and to amplitude that is going to be displayed on the oscilloscope.

Here we generated a sinusoidal wave using a 96 Hz frequency, using the amplitude control we increased the amplitude of the since wave.

Here is the mystery box we were given after using the wave function, we used two inputs to observe what type of waves would be produced by the box.

Here were the differing functions we found using the mystery box had quite similar waves with varying periods determined by an unknown frequency.

 

Charging and Discharging a Capacitor

Capacitors carry a charge and a potential that vary with time, using Kirchhoff's loop rule we experimented with a circuit to observe how a capacitor charges and discharges and what factors determine why they do.

 

Here we derived the time constant T (tao) which was equal to 1/R*C ( resistance and capacitance)

This factor was used in relation with the derivation of the loop rule E-iR-q/c=0 solving  for current

 we found that the charge q=Qf(1-e^-t/RC) was the equation for a charging capacitor with the factor T (tao) determining how fast the capacitor charged and discharged.

       Here was our circuit set up , we used a resistor of 3.5 kohm and a emf of 4.5 V. We ran our         capacitor in series to see how it charged and ran the circuit in parallel to see how it discharged.


We used sensors on the capacitor to record the current through and charge on the capacitor as shown below

 

 

 

 

 

We used Logger-Pro to display the relationship between the current and the charge on the capacitor once a current was introduced to the circuit, what we observed was as the charge increased on the capacitor the current decreased as a result of the potential between the emf and the capacitor plate decreasing.

 

As a result of this lab we found that initially when the circuit was closed the charge and potential across the capacitor was zero, after a time the charge increased as a result of the current carrying charge to the capacitor, the current decreased as the electric potential decreased.

Capacitors 1

Capacitors are used to store charge and therefore store potential in the electric field between the equal in magnitude but opposite in charged conducting plates. The given equation we are searching for capacitance is C=Q/V

We used foil as our conducting plates and printer paper as our dielectric ( the medium through which our electrostatic field will be transmitted through). We used a voltmeter to calculate the potential difference between the plates.

During this experiment we added paper between the plates to observe how added distance would effect the capacitance given the same dielectric, charge, and area.

We found that the capacitance of a rectangular plate was proportional to area of the plates, the distance between them, and the permittivity of free space or in our scenario the permittivity of the dielectric (printer paper).

Here is our calculations that we plugged into excel to generate a function displaying the inverse relationship to distance that capacitance has.

 Calculating equivalent capacitance of various capacitors in series and in parallel in a circuit analysis is important to understanding how a certain circuit values can be calculated. Capacitors in series add inversely while ones in parallel add directly.

Loop Rule Bread board

 

Using Kirchoff's laws for circuit junctions and  circuit loops, which states for a junction the total  amount of current entering a junction has to equal the total amount coming out, the loop rule uses the  principle of the conservation of energy to calculate the total potential across the circuit loop. We used a bread board and a diagram to build a circuit and test whether it correctly transmitted current properly. 

 

Given a generic circuit containing  resistors and sources of electric motor force (emf) we used Kirchoffs rules to calculate the potential across a resistors as well as current across a resistor. We created equations which we solved using the systems of equations technique.

 

Here we used a emf source in this case a 9 volt battery, varying resistors ( 3.6 kohm, 2 kohm, 2.2 kohm) and voltmeter to create circuit and test the current through the resistor and the potential drop off that occurs internally in a resistor.

During this lab we conducted various experiments to validate Kirchhoff's laws and how they apply to circuits in real life and theoretically given certain components and voltages.

Potential Distributions

 

 

During this lab we calculated various potentials due to various objects. Starting with a charged ring we used V=k* Sum dq/r for a point a finite distance from the axis of the charged ring. After some calculations we found it to result in k*Q/(x^2+a^2)^2

We had to calculate the potential difference caused by different charge distributions and different locations of our field points where the potential was to be calculated. We used the definition of the potential at a given point a given distance from a given charge distribution.

 

We used conductive paper, a voltmeter, and DC supply to calculate the potential between to conductive lines of a positive charge and at the opposite end a negative charge. We used the voltmeter to calculate the potential based on various displacements.

 

Using excel to calculate the potential difference with varying distances











Throughout this lab we verified how the value of potential varied with distance and location of a charge as well as charge distributions.