Day 27 RLC Circuits

At the beginning of the class, we started off by finding what happened to Irms if we double the w (omega). And we got that Irms also increase double.

This is an experiment when we needed to measure Irms and Vrms to calculate theoretical Z and compared with the actual Z

This graph shows V and I, and the box on the line is how we gather our data for Vmax and Imax.

In the data table about, we compared the theoretical Z and actual Z difference for  10 Hz frequency and 1000 Hz frequency. For 10 Hz, the percent error was 8%. But for the 1000 Hz, the percent error was 773% which was incredibly high.

This is the graph of current of 1000 Hz. And this is the best graph we could get because the frequency was so high, and we had to measure V and I separately to get the right data.

Then we calculated the angle because two frequency by the equation shown in the picture.

We used another equation to calculate the angle again, and the results came out almost the same.

Then we started to do a problem on RLC circuit. We calculated the frequency as 5033 Hz in the circuit.

For the 3000 Hz, we found that the Irms is 2.06A by the equation Vrms/Z. 

This is the equation to calculate power in this circuit because resistor is the only thing dissipates power.

Then we did another experiment about RLC circuit.

We used multi-meter to find that V and I, and calculated that Zexp is 15.5

Conclusion

In today's class, we were introduced Vrms, Irms, and Z. We also learned and did some experiments on RLC circuits.

Day 26 Alternating Currents and Voltages, AC Circuits

At the beginning of the class, the graphs of alternating currents and voltages were showed to us. They are both trigonometric functions.

These are the relationship between Vmax and Vrms; and Imax and Irms.

We did a practice problem on Vrms and Vmax by the formula provided in the picture.

Then we started doing an experiment on alternating currents and voltages. 

We used logger pro current probes dual channel amplifiers, functional generator, resistor using the RLC circuit board, and a digital multimeter. 

These are the graphs for alternating currents and voltages.

These are the results of our experiment. 

We used the equation of V to find Ic(t) and found that Ic(t) has bigger amplitude than V.

We were given c, frequency, and Vrms, and we needed to find Xc and Irms.

Then we started doing an experiment on Capacitors in an AC circuit.

We used the vernier logger pro voltage probe current probe dual channel amplifier, functional generator, and RLC circuit boad where C1 = 100 uf and C2 = 150 uf.

These are the graphs we got. We found that Vmax = 2.005 V and Imax = 0.116 A.

These are the data we recorded. We got the percent error of 18% on theoretical capacitive reactances and experimental capcitive reactance.

We calculated the Xc to Irms.

In the picture, we derived the equation I = (-Vmax/wL)*cos(wt+ø)

We used given data to calculate XL and to calculate Irms.

Last experiment we did today was the Inductors in Alternating Circuits.

We used a 110 turns inductor to find L and then found XL.

These are the graphs for currents and voltages. We needed to find Vrms, Vmax, Irms, and Imax on it.

This is the data we recorded for this experiment. We got an percent error of 12.5 %.

Conclusion

For today's class, we learned about alternating currents and voltages, and different cases in a AC circuit. We learned Capacitors in a AC circuit and Inductors in AC circuit.

Day 25 Inductance, RL Circuits

At the beginning of the class, inductance is introduced to us. This picture shows that any change in the current through an inductor leads to a change in the magnetic field it produces.

This is the current vs. time graph when an inductor presents in the circuit.

The professor gave us a 100 ohm resistor that has brown, black, and brown pattern on it. 

Then we calculated the inductance by the formula shown in the picture.

We also calculated the time constant τ = 5.1*10^-6 s.

This τ is given by professor which is 2.55*10^-5 s

In this picture, we started to do an experiment on the Oscilloscope

We set up the functional generator and make it display the graph in the right picture

Then we calculated the inductance by two different equations. By the top equation, we got 760 mH, and by the bottom method, we got 736 mH

Then we were introduced to a LR circuit problem

We solved for resistance, τ , current, voltage, and energy of the circuit.

Conclusion

For today's class, we learned about inductance, oscilloscope, and LR circuit. We did experiments and problems to get used to them.

Day 24 Motional EMF, Maxwell’s Equation and Induction

At the beginning of the class, we did an online activity that has 13 questions about EMF.

In this activity, there is a magnet connected to the current. And there is a copper stick in the middle of the magnet. We predicted that as the current is on, the stick will roll out.

This is a short video shows the result

In this picture, we drew a graph to show what happened in the system for the activity. And if the current is inverse, the force will be inverse also.

Then, we did another 13 online activity problems on motional EMF

The Maxwell's equations were introduced to us!

In this picture, we were deriving the equation of I = C dv/dt by using V = L dI/dt, V = RI, and C = Q/V

Then by the equations of magnetic field and flux, we derived the equation for inductance (L)

Then we did a practice problem on finding inductance.

We were looking the unit of inductance and we got kg*m^2/C^2 which the actual unit is called Henry (H)

Then we begin to learn RC circuit, on the left is the circuit that has an inductor. On the right is the I vs. t graph which represents when t increases, V and I are 0, and then rapidly increase.

In this picture, we find the time constant τ = L/R

Then we did a practice problem based on τ.

Conclusion

Today in class, we learned about EMF induced, Maxwell's equations, motional EMF and inductance. Also, we did some problems that involve inductor and τ.