RLC circut and Transformers

Resonance in RLC Circuit

SET UP

An RLC circuit was set up and for the first part of the lab.  The values of the inductor, resistor, and capacitor were found using a multimeter, then the theoretical resonance frequency was solved for using those measured. The experimental resonance frequency was found using the function generator and a multimeter and measuring the frequency that holds the max current.

Parts 1 & 2

For part two, the experimental impedance was found with the measured values from the multimeter and the formula Z=((R^2 + (Xl-Xc)^2)^1/2. That value was compared to the theoretical value of impedance; Z=R. Our percent difference was nearly 0!

For part three, the theoretical frequency and experimental frequency were found using LoggerPro. As we can see on the graph, there is a phase angle difference of 180 degrees. If the frequency was increased, the amplitude decreases when measuring across the capacitor and the amplitude increases when measuring across the inductor. (See white board photos below) 

Transformers

A transformer is made of two inductors linked together by an iron core (not a giant crime fighting robot). The iron core redirects magnetic flux in one inductor to the other. Eddy currents are currents created by a changing magnetic field which are undesirable. The Eddy currents produced increases energy lost. A solution to this is laminating the plates of the metal. The lamination reduces the size of the induced loop and therefore reduces the amount of energy lost.

Resistors, Capacitors, and Inductors in an Alternating Circuit

Resistors in an Alternating Circuit 

Set Up

A resistor was hooked up to a function generator which was producing a 200 Hz sinusoidal wave, and current meter in series. Attached to the resistor was a voltage meter.  In order to calculate the theoretical Irms and Vrms, the Imax and Vmax were taken from the LoggerPro graphs and divided by squrt(2). Using those values, percent difference was calculated for the voltage and current. It can also be seen that in the current vs potential graph that there is no phase change within the voltage and the current with the linear relationship.

Poential vs Time

Current vs Time

Potential Vs Current

Calculated and theoretical values

Capacitors in an Alternating Circuit 

The same set up from the resistor was used expect now the resistor has been replaced with a capacitor. In AC circuits, capacitors exhibit a resistance which is given by Xc= 1/wC where w(omega)=2 pi f (frequency).

Set Up

Data was gathered using logger pro and a Potential vs. Time, Current vs. Time, and Potential vs. Current were generated. The Vmax and Imax were taken from the graphs and used in order to find the Vrms and Irms. Using the formula for reactance, the theoretical and experimental values were found and the percent difference was calculated. It can also be seen from the graph of current vs potential that the current and potential are out of phase approx. 90 degrees by the circular relationship.

Graphs

Theoretical and Calculated values

Inductors in an Alternating Circuit

Set up W/O iron core

The same set up was used, however, now the capacitor was replaced with an inductor. Data was gathered using logger pro and a Potential vs. Time, Current vs. Time, and Potential vs. Current were generated. Calculations of Vrms, Irms, and Xl were made and the experimental resistance of the inductor was calculated and the theoretical inductance was found with a volt meter (by Professor Mason). The percent difference was found to be 98%.

It can also be seen by the potential vs current graph that the current and voltage are out of phase approx. 90 degrees by the circular relationship.  The circle isn’t perfectly round because of there not being an iron core in the inductor and therefore reducing the value of the inductance and reducing the lag of the voltage and current. 

Graph w/o iron core

Set up with iron core

For the second part, an iron core was added to the inductor and the same steps from part 1 were followed. In the end, a 41% difference was calculated, a much lower percent difference than without the iron core. This is due to the iron core increasing the inductance without changing the resistance.  The circle is also more round due to the phase shift being closer to 90 degrees.

Graphs with iron core

Work for iron core and w/o iron core

RC in an Alternating Circut

A resistor and a capacitor were hooked up to a function generator and a current meter and volt meter were connected to LoggerPro. Data was gathered using logger pro and a Potential vs. Time, Current vs. Time, and Potential vs. Current were generated. Using the graphs the Vmax and Imax were found and the Vrms and Irms. The total resistance within the circuit is the total impedance, or Z was found and so was the time phase change based on the graphs. The percent difference was found for the impedance as well as for the time phase change.

ActivPhysics (Inductance), Measuring Inductance

ActivPhysics (Inductance)

We performed an ActivPhysics to help us better understand Inductance.  Answers to questions 1-8 are on the whiteboard below.

Measuring Inductance

Set Up

We created a circuit with a function generator, a resistor, an inductor, and an oscilloscope.  All of the data collected throughout the lab is recorded below on the whiteboard.  What the oscilloscope shows us is a qualitative plot of the potential differences across the inductor vs time and is also how we solved most of the problems in the lab.  Uncertainty was also found for #8 and #9 (whiteboard below)

Graph from oscilloscope

Answers and Work

Uncertainty for 8 & 9 

Force Due to a Magnetic Field, Magnetic Field in a Solenoid, Lenzs’ Law, Faraday’s Law, Magnetic Induction

Force Due to a Magnetic Field

Set Up

In this demo, two wires are placed next to each other and connected to a voltage source. The force due to the magnetic field from wire 2 on wire 1 is solved by the definition of magnetic force current and magnetic field

The current is sent the same direction through the two wires and it was predicted that the wires would move away from each other, however, the wires move towards each other. This can be determined by the right hand rule with the thumb and curl of the fingers. The magnetic field travels in a circle around the wire, but we only care about the part of the magnetic field that hits the other wire tangentially. Using the right hand rule, it can be see that the forces are both pointing towards each other.

Predictions and Answers

When a current is run through each wire in opposite directions, it was predicted to repel each other and it did which was also determined by the right hand rule. 

Magnetic Field in a Solenoid

A magnetic field sensor was used to determine the magnetic field inside of a solenoid.  Wire was wrapped around a test tube and the magnetic field produced by that circle of wire was measured with the field sensor on logger pro.  It can be seen that the magnetic field in a loop is proportional to the number of loops and the current running through the loops. It can be seen that the more loops added, the higher the magnetic field.  Also, the closer together the loops were the bigger the magnetic field was as well. The maximum magnetic field was seen at the end of the solenoid (test tube with wires wrapped around) when the magnetic field was parallel to the area vector.  

Lenzs’ Law

Lenzs law states that a magnetic field always opposes an induced magnetic field and this experiment was to prove that. Two cylindrical objects, one magnetic and one nonmagnetic, are to go through two tubes at the same time.  One of the tubes is made of aluminum and the other is plastic. It was predicted that when the magnetic object is dropped in the aluminum tube it would fall faster because in a conductor, the electric field is equal to zero. However, the magnetic object fell faster in the plastic tube and much slower in the aluminum tube. The magnet induces a current when it moves through the aluminum tube and therefore induces a magnetic field. According to Lenzs' Law, the induced magnetic field points upwards in the opposite direction as the magnetic field and slows the fall of the magnetic object. When the magnetic object is placed in the plastic tube they fall at the same time because the plastic tube isn’t a conductor and therefore no current or magnetic field is induced.

Faraday’s Law

Faradays law states that in order for there to be a flux there must be some change in either the magnetic field, area, or the angle between the magnetic field and area vector is changing.  

Effect of magnetic field changing

smaller area bigger current

This demo was to see if magnetism could create an electric field capable of causing current to flow in a wire.  We tested this by connecting a coil of wire to a galvanometer.  When the magnet was inside the coil of wire, no current was produced.  We determined that the magnetic field must be changing in order to create a current.  We then determined five different ways to maximize the current (see whiteboard for details).

larger area smaller current

Effect of area changing

A large amount of current was applied to the rails of the system shown in the picture of the set up.  When you apply the current to the rod, the rod slides backwards.  What is happening can be explained by one of the right hand rules with the pointer finger, middle finger, and thumb.  When you point your fingers in the direction of the current and magnetic field it can be seen that the magnetic force produced is pushing the rod backwards.  This applies to Faraday's Law because the area of this closed loop is changing while the Magnetic Field being produced by the large magnet at the end of the system and the current flowing through the rod is constant.   

Magnetic Induction

In this demo a current was ran through a coil of wire and when an aluminum ring was placed on the energized coil, the ring began to levitate which means there must be some force acting on the ring.  After taking the ring off the coil it was observed that the ring was warmer than before which is because when the ring was placed on the coil an induced current was flowing through it.  The coil has and original current in it and creates magnetic field going up.  This magnetic field is making an induced current in the ring which is going in opposite direction of the current of the coil.  This current flowing through the ring creates a magnetic field in the ring opposing the magnetic field produced by the coil.  We now have two magnetic fields repelling which is why ring levitates because of interaction between mag field in coil and in ring.

Now we replace the initial ring with another aluminum ring that has a slit in it.  No current can flow through this ring because of the slit which results in a ring that doesn’t get hot which is because there is no current going through it.

A light bulb is attached to a solenoid and put over initial coil that has a current flowing through it and a magnetic field which induces a current and magnetic field in the solenoid above the initial coil and lights bulb.

In an oscilloscope

A function generator was connected to a large coil which was connected to channel 1 of the oscilloscope.  A smaller coil of wire was placed in the large coil and then connected to channel 2 of the oscilloscope.  The image displayed from the large coil is a large sine wave and the image displayed from the smaller coil is the exact same sine wave except for it has a smaller amplitude.  The reason they have the same current flowing through them is because the large coil is educing a current and magnetic field in the smaller coil.  It can be seen when you turn the coil on its side so the holes are now laying horizontally, then the current in the smaller coil is now zero because the magnetic field and the plane of the loop are perpendicular (they must be parallel).  It can also be seen that when you move the smaller coil in the larger coil and move it towards the edge of the larger coil, it can be seen that the current is larger.

Electric Motor, Building an Electric Motor, Magnetic Field Near a Current Carrying Wire, Magnetic Fields from Different Wiring Arrangements

Electric Motor

Answers to Electric Motor Worksheet

Answers to Electric Motor Worksheet

Answers to Electric Motor Worksheet

Stint Louis Style Motor

(example of the motor used to answer questions in worksheet above)

Motor without split ring communicator

There are two coils of wire that when connected to a voltage source make a magnetic field. The motor will continue to spin until the magnet is lined up with the magnetic field.  In order to keep the motor spinning you must alternate the magnetic field or the current. 

Building an Electric Motor

Using copper wire spun into a circle, paper clips, magnets, and a voltage source, an electric motor was created.  We sanded down 180 degrees on one side of the copper wire and sanded down 360 degrees around the other side of the copper wire.  We did this so we could get an alternating current in our wire and therefore keep the motor spinning. 

Magnetic Field Near a Current Carrying Wire

When you place numerous compos's around a current carrying wire it can be seen that the electric field goes in a circle.  This gives us another right hand rule.  Your thumb is the current and your fingers are the magnetic field and the magnetic field either points in clockwise or counter clockwise

Magnetic Field going Clockwise

Magnetic Field going Counterclockwise

Magnetic Fields from Different Wiring Arrangements

We were to find the magnetic fields at the different marked spots.  It can be seen that when currents are going opposite ways, the magnetic fields cancel out which is why when you're wrapping wire for a motor you shouldn't cross your wires.  When the currents are going the same way then the magnetic field is twice as big because there is twice the current.   

NO CLASS!

Field Directions Around a Bar Magnet, Oscilloscope Demonstration, Magnetic Forces and Electric Currents, Forces in a Curved Wire

Field Directions Around a Bar Magnet

A compass was placed around a bar magnet and the magnetic field lines were marked.  It can be seen that the magnetic field runs from the positive (North) to the negative (south).  

Also, if you pour iron over the bar magnet they form around the magnet in the shape of the field lines which ran from the north to south pole.

Gauss’s Law for Electric Charge

You cant have only one pole in the imaginary surface, you must have both poles enclosed therefore the net flux is always zero.

Oscilloscope Demonstration

We observed the effects of a magnetic field on an electron and we determined that the way the electron is moving is perpendicular to the direction of the magnetic field and when the magnetic field approaches the electron parallel then there is no effect.

The right hand rule can be used to find the direction of the force, current, or magnetic field where the thumb is the force, the finger is the current and the middle finger is the magnetic field.

Magnetic Forces and Electric Currents

We observed the effects that a magnet had on a non magnetic wire that carries  a current using Lorentz force.  The way we initially had the circuit set up the wire jumped up because of the direction of the magnetic field and the current going through the wire.  We reversed the current through the wire and the wire now gets pulled down.  

magnet being pushed up

magnet being pushed down

Forces in a Curved Wire

A spread sheet was used to find the using Lorentz force I*dL*B*sin(theta) and the forces were summed up to find the total force on the section of the curved wire which we found to be .70 N