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.