LRC Circuits(0602)

LRC Circuits

We derived formula for I_rms from V_max. Notice here we used X_L and X_C that we learned from last Thursday. If we double the omega, the current also doubles

Our lab result R-C circuit with A-C current, the higher the frequency, the higher percent error

Here we found the phase angle by using tan^-1 (X_C/R)

Finding the dissipation Power (the power that only involves resistor)

The logger pro's graphs of current v.s time. Here we had to measure current and potential one at the time so we can measure at high sampling rate, which gives better graphs

Here, Z=R since the current has frequency= resonance frequency. We found the experimental impedance to be higher than theoretical impedance. This could be due to our approximation of A-C current.

AC Circuit (0528)

AC Circuit

We derived the formula of V_rms= sqrt (V_max)

This is our set up

The sinusoidal wave function of potential and current with respect to time.

AC Circuit

In the circuit that only has the capacitance in series with the voltage source. I=C*dV/dt. Since V equals to sinusoidal function, we expect I to have cosine function with bigger amplitude (assuming wt>1)

Here is a simple problem we were assigned to do. Our job is to find X_c= 1/(wc). X_c, interestingly, has the unit ohm as resistance

We set up the resistor is 100 omh and voltage is 2V, and use the graph to find the V_max and I _max and use the equation V_max=square root 2 *V_rms, and I_max= square root 2*I_rms. to find the V_rms and I_rms.  and use 2V and 100omh to find the theoretical V_rms and I_rms and find the error of them.

After several trials. We found I_rms and V_rms for both theoretical and experimental

We were given a practice exercise. For this problem, we had to find reactant and I_rms. 

Here is our calculation for activity inductors in AC currents.

Introduction to inductance (0526)

Introduction to Inductance

First, we reviewed the Faraday's Law of the inductance. Here we wrote the wrong equation. It should be L= flux B /I. We also need to get 100 ohms resistor, which has the color code of brown black brown.

Here first we were trying to find the resistance of the coil using rhp*length/A. Since B of toroidal solenoid is B= miu_not*N*I / (2*pi*R), we derived L as seen above.

After we found the inductance L=miu_not*N^2*A/l

Our approximation is about 72 turns, which more 22 turns compared to 50 turns of the solenoid

WE used 40khz, with 2V and 0.02A as our source.

Here Professor Mason uses the formula of growing current in L-R circuit. He first calculated I_max and I_0. then use I(t)=Imax*(1-e^-t/tau)

Here we did almost the same as Professor Mason did. But since V mas is 0 not emf. This way is wrong mathematically.

Here we were trying to find the potential energy in this circuit, the time is 170us. The U_1 is belong to the inductor= 0.5*L*I^2, since the time is pretty quick, we can assume that the power dissipated in R_1 is negligible. Therefore, U_2=V_2^2/R*t.

Magnetic Field, Inductance, RL-Circuit(0519)

Magnetic Field, Inductance, RL-Circuit

Predict the direction when the current through the bar.

We explained the simple mechanism of the rail gun by applying the right hand rule.

Formula derivation for the rail gun. Since the area is changing with time, we write it as A(t)= A_0+ vLt with v is velocity and L is the length of the bar. Since emf depends rate of change of flux  and rate of change of flux depends on rate of change of A. emf has to depend on velocity

Here we kept doing the activity online. Since dA/dt= vL, We have emf=vBL.

L here is inductance= V/ (dI/dt). We know that C=Q/V. We can I= C* (dV/dt). By following the derivation we did on the board, we have L=- N^2*miu_not*A/l

SI unit of Inductance is Henry (H)=  km*m^2/C^2

Here we have current as horizontal graph. The voltage has an exponential curve.

Here we derived formula for tau from L and R. Recall that I=I_0 (1-e^-t/RC) to get tau=L/R.

Lenz's Law and Faraday's law (0514)

Lenz's Law and Faraday's Law

After we had the direction of the magnetic field, we could use the regular right hand rule ( of three vectors) to find the direction of the force. Interestingly, the magnetic forces will pull the wires together ( for DC source).

Then the professor shows us the experiment. When closing the switch, and the two lines were charged, they get closer thant no charged.

Then we make a prediction, we think that because there are forces that makes them closer, but actually, because of the power is alternating current, so there is no force.

Then in these two photos, the professor use logger pro to make a graph of the change of magnetic field as time changes. and we draw the north and south poles in the graph.Professor then performed the experiment by switching on the power supply causing an alternating current in the two parallel lines. There are in fact no net forces acting as there due to the alternating current. Then he uses logger pro to show magnetic field in respect to time.  Two cycles here are observed in which we can interpret the magnetic field oscillations caused by the north and south poles by applying Faraday's law

We use logger pro to collect data and make a graph in this photo,

in this photo, we calculate the flux of magnet. the first one, because the B and A are parallel, so the flux is 0, and the second one, because they are perpendicular so the flux=B*a*b

The professor use a magnet to cross the loops and when it enter or leave the loops, the dash board will change. Professor uses a bar magnet and galvanometer and allowed the magnet to go back and forth causing movement (changing magnetic fields) which stimulates a current seen in the movement of the meter through induction. As he stops in the center of the coil there is no change in the meter when it stay in the loops, it doesn't change 

We list 4 reasons that can influence the dash board.If we want to maximize the current on an induced EMF we can add more loops on the coil, have a bigger loop by increasing the area, use a bigger magnet, and also move the magnet faster

Then we use this equipment in the photo to see what will happen

Then in this photo, we draw the graph of force, magnetic field. When the north pole of the magnet is going toward a loop, the flux increases and an upward secondary magnetic field is created causing a counterclockwise current. The changing flux created by the magnetic field created by the induced emf causes the the loop to float due to the force upward.

In these two photos, we first find the E that created by the moving of magnet and draw the two graphs of B and E

Summary:

     In today’s class, we learned Lenz's Law and Faraday's Law to see how we could induce a current using magnetic fields and magnetic fields, forces, torque, and flux. find that an EMF and flux explains the relationship between the two by using Lenz's law and Faraday's Law to magnetic fields. We did many experiments that made a steel ring and we saw that the forces of the magnetic field create some objects to levitate just like the rings.

Magnetism, Electricity and Motor(0512)

Magnetism, Electricity and Motor

We predict two ways to destroy a magnet. one is heating and another is hitting it.

Heating up

In this photo, we begin to do another exercise, make the loop galvanical and give it a magnet field, the direction is upward. Then we find that only the top and bottom lines has Force and the net force is 0.

Then we use the equation torque=F*r ,and F=BIL to find the torque=1/2BIL^2, and the net torque is BIL

This question is a little tricky. Theta is actually the angle between the normal vector B and the the plane, therefore the angle we used would we 90-theta, not theta.

This picture is the inside of motor.

Our demonstration of right hand rule. Notice that the thumb points in the direction of the current.

The above 2 pictures are from an experiment we did if we had a current going through the metal pole in the center of a box surrounded by compasses. We found that the current produces a magnetic field causing the magnets to point in a counter-clockwise direction around the metal pole. This matches our right hand rule along a current.

We equated two equations F=qE=qV_d xB (recall that V_d is drift velocity). We then find the current by using the drift velocity formula we had learned before to find the V_H

Here we  were tryiing to find the magnetic at the specific points inside the loop. The dots described the fingers are coming out, and the crosses described the fingers are coming in.

Universal constants given is epsilon_not and u-not. Interestingly, F_B/F_E is v^2/c^2. Therefore, if the object approached speed of light, the magnetic force and the electric force would be the same.

This is the video we made and shows the success of this small electric motor.

Summary:

     In today’s class, we learned a lot about magnetism and the properties that are inside the magnets and how they interact with the other.  We learned that torque is generated in a current loop in a magnetic field due to forces on the sides when there are N turns of wire. We learned about another right hand rule which shows us the direction of the magnetic field.  We learned how to create a magnet and how to destroy a magnet. We were also introduced to motors and use magnetic fields to rotate the motor. We also created a motor with a wires, paper clips, and a battery.