Day 24 APPARENT POWER AND POWER FACTORb

We started the day with a picture of the dance lesson for engineers a very fun picture. Then we move onto the effective RMS value. We were asked to the algebra with our current knowledge to see what we end up with.

White board work to find the RMS value of voltage.

We then had to calculate the RMS value of the sine wave. We transformed it and then did some algebra.

White board work to get the square root of 2.

We then talked about grpahed the phasors and talked about ELI the ICE man.

White board work below taking about ELI the ICE man. Which means Voltage leads current in a Inductor, and Current leads Voltage in a Capacitor.

We then talked about apparent power and power factor. We used pf = P/S, we then did an example below.

White board work of an example, left side, first step is to transform to phasor domain.

More white board work continued.

White board work, right side, once we got Z we can get pf, and we have S so now we can get P = Spf.

We then move onto to talk about complex power. S = 1/2VIconjugate. Z = V/I = Vrms^2/Zconjugate. The following interesting comes form that which ar, S = P +jQ, P = realS and Q = fakeS.  For pf if Q = 0 the load is unity for pf., Q < 0 capacitive load, leading pf, Q > 0 inductive load, Lagging pf. We then talked about the triangle of SPQ and tried an example.

White board work of the example. Get things to phasor domain, use P and Q, find S = sqrt(P^2+Q^2)

More white board work continued.

White board work of complex power example, used the rules mentioned above.

We then talked about power factor correction. We used:

Q _C = Q ₁ − Q ₂ = P (tan θ ₁ − tan θ ₂ ),

Q _C = V²_rms/X C = ωCV²_rms 

Q _L = Q ₁ − Q ₂ 

With this knowledge we tried an example below.

White board work below, using what we just learned, we found C = 310uF.

After that we move to the lab of the day: Apparent Power and Power Factor!!!
Prelab: White board work of the pre lab. All of our Prelab numbers are in the picture we never got around to tablet in one place.

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Picture of the Vin blue, Vout yellow, Red current.

Picture of data for first signal C2 in, C1 out. Vampin = 1 V, Vinrms = 710 mV, Voutamp =  864 mV, Voutrms = 610 mV, Iout = 19 mA, Iin = 30 mA we used another math channel for S which we got S to be 2.5 V. Freq = 5 khz.

Picture of the first circuit. Rt = 10, Rload = 10.

Picture of circuit, of Rload = 10 ohms.

Picture of signal at next Rload of 47 ohms.

Picture of Vin blue, Vout yellow, Current red at 47 ohms.

Picture of data for R = 47. C2 in, C1 out. Vinamp = 1.01 V, Vinrms = 714 mV, Voutamp = 820 mV, Voutrms = 578 mV, Iin 20 mA, Iout = 13 mA, S = 2.66 W, freq = 5 khz.

Picture for Rload = 100 ohms.

Picture of Vin blue, Vout yellow, Current red at 100 ohms.

Picture of data for Rload = 100. C2 in, C1 out. Vinamp = 1.01 V, Vinrms = 720 mV, Voutamp = 872 mV, Voutrms = 616 mV, Iin 14 mA, Iout = 10 mA, S = 9.7 W, freq = 5 khz.

We then added a 1uF and redid all three loads again.

Picture with 1uF and Rload of 10 ohms. Vinamp = 1.01 V, Vinrms = 583 mV, Voutamp = 826 mV, Voutrms = 717 mV, In = 19 mA, Iout = 13 mA, S = 7.33. It is higher S with new 1uF when compared to the old S.

Picture of the circuit with capacitor and 10 ohm.

Picture of circuit with capacitor = 1uF an Rload = 10 ohms.

Picture of Rload for 47 ohms.

Picture with 1uF and Rload of 47 ohms. Vinamp = 1.01 V, Vinrms = 531mV, Voutamp = 750 mV, Voutrms = 531 mV, In = 29 mA, Iout = 20 mA, S = 2.54. It is lower S with new 1uF when compared to the old S.

Picture of Rload = 47 ohms circuit with the capacitor.

Picture of the circuit with Rload = 47 ohms.

picture of the signal and data for Rload = 100 ohms.

Picture with 1uF and Rload of 100 ohms. Vinamp = 1.01 V, Vinrms = 568mV, Voutamp = 717 mV, Voutrms = 568 mV, In = 24 mA, Iout = 16 mA, S = 6.54. It is lower S with new 1uF when compared to the old S.

Another picture not sure of which Rload.

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Picture of the Rload = 100 ohms with the capacitor.

My picture again with Rload = 100ohms

Data for Rload = 100ohms

Picture of Rload = 47 ohms

Picture for Rload = 10 ohms

Data for Rload = 47 ohms.

Picture for Rload = 10 ohms

Data for Rload  = 10 ohms.

In conclusion this lab was long and difficult going back to this lab I was lost with the pictures. It could be that we went from 10, 47 to 100 ohms or 100, 47, to 10 ohms with we took pictures for the capacitors added system. All data required should be seen on the Data version of the pictures.

White board picture of the lab completed with a Grade of A.

In summary we started the day with talking about the different dances of function and went to really talk about rms. We found rms to be whatever we have divided by sqrt(2) from the algebra and integration of power. We then did some graph manipulated to end up with the same answer. We talked about apparent power and average power and move onto complex power. Lastly we ended the day with the lab covering everything we just learned. The lab had a lot of parts and our power found made sense when we added the capacitor to the circuit.