Lab Report Day 23 - Apparent Power and Power Factor

This lab assignment emphasizes the use of apparent power and power factor to quantity the AC power delivered to a load and power dissipated by the process of transmitting this power. Our goal in is to provide some necessary average power to load with minimum power lost during the power delivery process. 

To do that, we will used a 10 ohm resistor, and a series combination of 1mH inductor and resistor (10 ohm, 47 ohm, or 100 ohm) resistor to be the load. We use a sinusoidal wave with (1cos(2pi*5000t) in the circuit and calculate the power dissipated by the resistor. 

This is the set up of the lab. 

We measure the resistors to be 11.9 ohm (10), 48.6 ohm (47) and 99.8 ohm (100). Number in "()" are theoretical values. 

Those are results and calculations. The resistance is series with a load that changes each time. We measure the voltage of the load and the voltage across the resistor in series with the load.

The oscilloscope screen with 11.9 ohm resistor

The oscilloscope screen with 48.6 ohm resistor

The oscilloscope screen with 99.8 ohm resistor

This is our measured value. The phase difference are very big. 

Then we include a capacitor in parallel with the load. This can make the voltages measured more in phase.

The oscilloscope screen with 11.9 ohm resistor with a capacitor

The oscilloscope screen with 48.6 ohm resistor with a capacitor

The oscilloscope screen with 99.8 ohm resistor with a capacitor

We can see that the phase angles are very small, less than 3 degrees for each.


Summary:

Today we are told that the electric company charge us with peak voltage instead of average power, and later we are told how to avoid it. All we need to make it more efficiency and draw less current from the power source is to add a capacitor parallel to the load. Therefore, that will. And we do a lab to prove this.

Lab Report Day Twenty Two - AC Average and Maximum Power

Today, we do not actually do any labs. But professor Mason uses a demo to show us how AC power works visually. 

This is a picture that when professor Mason uses AC power and DC power to light the bulb at the same voltage. We can clearly see that the one with AC is dimmer. It shows that the bulb with AC has less power. 

When professor Mason turns the voltage for AC to about 1.4 times of the DC power, they seems the same bright. This proves that Vrms = 1/sqrt(2) Vmax. The voltage we read is Vmax instead of Vrms. 

It proves that power of AC is P=Vrms^2/R. 

Summary:
Today we review inductor and average and maximum power calculation in a  AC circuits, and see a demonstration to see how rms values dictate maximum power of AC circuits.

Lab Report Day Twenty-one - Inverting Voltage Amplifier, Op-Amp Relaxation Oscillator

Inverting Voltage Amplifier

In the first lab of the lab, we build an inverting voltage amplifier using an op-amp.  We first calculate the theoretical voltage gain and the phase shift.

We first derive the formula we are going to use. 

We use 2 10K ohm resistors, 1 1 uF Capacitor, and 1 Op Amp to build our circuit. 

Input and output voltage at 100 Hz. 

Input and output voltage at 1k Hz. 

Input and output voltage at 5k Hz. 

This is our result table including the theoretical value and experimental value of gain and phase different at f=100 Hz, 1K Hz, and 5k Hz. 

This is a brief summary table.

 Op-Amp Relaxation Oscillator:

In this lab, we first construct a relaxation oscillator on EveryCircuit.

We are going to generate a frequency of 99 Hz. We calculate the theoretical value for the pot to make this work to be 8371 ohm.

 The circuit consists of 1 10K resistor, 1 100 ohm resistor, 1 10k POT, 1 OP 27, and 1 0.1 uF capacitor.

This is the out put of the circuit. The frequency is 99.8 Hz. It has a percent difference less than 1%. We do this lab successfully.

Summary:

Today we go over how OP Amps work in AC circuit, and do labs to see how to see how they can apply in real life. We learn how op amp relaxation oscillator works and how we can make our desired frequency. 

Lab Report Day Twenty - Phasors: Passive RL Circuit Response

Phasors: Passive RL Circuit Response

 

In this lab assignment, we measure the gain and phase responses of a passive RL circuit and compare these measurements with expectations based on analysis.

 

In the pre-lab, we predict the amplitude gain and phase difference with 3 different frequency: Wc, Wc/10, and 10Wc, where Wc is 2.2*10^5 Hz. We also find the cutoff frequency for the circuit. When W= Wc, we expect amplitude gain = 0.0321 and expect phase difference = -45degree. When frequency = Wc/10 expected amplitude gain = 0.0452 and expected phase difference = -5.711 degree. When frequency = 10Wc expected amplitude gain =4.52*10^-3 and expected phase difference = -84.3 degree. 

 

We use a 22 ohm resistor and a 100 uH inductor to build the circuit.

At f=35k Hz, Vin=989.4 mV, and I=31.25 mA. phase difference is -37.8 degree. Gain is 0.0316. 

At f=3.5k Hz, Vin=973.4 mV, and I=38.55 mA. phase difference is -6.3 degree. Gain is 0.0452. 

 

At f=350k Hz, Vin=994.8 mV, and I= 5.665 mA. phase difference is -78.12 degree. Gain is 5.695*10^-3. 

 

This is a summary table of our experiment including our percent difference, experimental value, and theoretical value for phase difference and gain.

 

Summary:

Today, we analyze the steady-state response of electrical circuits from sinusoidal inputs. We can find the amplitude gain by comparing the Vin and Vout. We also learn how to analyze AC circuits using different methods of analysis including nodal analysis, mesh analysis, superposition, Thevenin and norton analysis. 

Lab Report Day Nineteen - Impedence

Impedance

In this lab assignment, we measure impedes of resistors, capacitors, and inductors. The measured values will be compared with our expectations based on analyses. 

In the pre-lab, we calculate the impedance for a RR circuit, RL circuit, and RC circuit.

 

This is the set up of our RR circuit. 

 

This is the RR circuit at 1k frequency. Vt= 1.354 V, I=13.2 mA. 

 

This is the RR circuit at 5k frequency. Vt= 1.354 V, I=13.2 mA. 

 

This is the RR circuit at 10k frequency. Vt= 1.354 V, I=13.2 mA. 

 

We determined the resistor impedance = 47 + R 

the real resistor values came out 46.6 ohm and 99.9 ohm, and therefore the experimental impedance for resistors = 146.5 ohm. 

We get our percent difference to be 0.34%. 

 

 

This is the set up for the RL circuit. 

 

This is the RL circuit at 1k frequency. Vt= 0.2652 V, I=40.05 mA. 

 

This is the RL circuit at 5k frequency. Vt= 1.0584 V, I=34.2 mA. 

 

This is the RL circuit at 10k frequency. Vt= 1.546 V, I =25.4 mA. 

 

The circuit is supplied with a 2V sine wave with different frequencies of 1kHz, 5kHz, and 10 kHz frequencies. In the inductor circuit the voltage leads the current by 90°. 

 

This is a RC circuit we build.

This is the RC circuit at 1k frequency. Vt= 1.999 V, I =1.05 mA. 

 

This is the RC circuit at 5k frequency. Vt= 1.9774 V, I =4.955 mA. 

 

 

This is the RC circuit at 10k frequency. Vt= 1.924 V, I =9.475 mA. 

 

The circuit is supplied with a 2V sine wave with different frequencies of 1kHz, 5kHz, and 10 kHz frequencies. In the capacitor circuit the current leads voltage by 90°

 

Summary:

Today, we analyze AC circuits. We find that a resistor AC circuit has no phase change between the voltage and current. The voltage leads the current by 90° in a circuit with an inductor and the current leads the voltage by 90° in a circuit with a capacitor. We learn that circuit elements can be represented as impedance.  

 

 

Lab Report Day Eighteen - Oscilloscope

Today professor Mason shows us how oscilloscope work. 

The following is a video of the lecture:

Video Credited By Sunny

On the oscilloscope, the screen is connected to a tube that is far back.

Inside the oscilloscope includes an electron gun. It contains wires and when we apply a voltage across it, the wire gets hot and emits electron in all directions. When we apply source with high intensity, some of the charges bounce around, some of the charges get absorbed, and some of the charges get shoot out the tiny hole and becomes electronic beams. The monitor projects the motion and position of the electronic beams. In the tunnel, we have a positive charged plate on top, and negative charged plate on the bottom, positive charged on the left, and negative charged on the right. When we apply voltage on the circuit, we can see the beam on the display screen. 

 

Summary

Today we about how an oscilloscope works. We learn how to convert sinusoidal waves to other form. This is important when dealing with AC circuit.

Lab Report Day Seventeen - RLC Circuit Response

RLC Circuit Response

This lab will emphasize modeling and testing of a second order circuit containing two resistors, a capacitor, and a n inductor. In this assignment, the step response of the given circuit is analyzed and tested. The measured response of the circuit is compared with expectations based on the damping ratio and natural frequency of the circuit. 

We built the circuit with a 1.1Ω resistor, a 47 Ω resistor, a 10uF capacitor and a 1 uH inductor. 47 ohm resistor and the inductor are in series while they are in parallel with the other components in the circuit.

 

This is the set up for the circuit. 

 

This is the input of our power. It is a square wave at frequency at 100 Hz, and amplitude of 2V at offset 0

This is the graph for V.

In the lab, the 47 ohm resistor has a real value of 49 ohm. The 1.1 ohm resistor has a real value of 4.3 ohm. The 10 uF capacitor has a real value of 9.92 uF, and we cannot measure the 1 uH inductor.  (In the picture, the 1 uF should be 1 uH.)

We calculated our experimental value of α to be 3588.7, while our theoretical value is 1063.8. It has a precent difference of -237.4%. 

 

Summary:

Today we learn how to analyze circuits containing a resistor, capacitor and an inductor in parallel. There are three possible cases that may occur in a RLC circuit which include over damped, underdamped, or critically damped. We also do a lab about RLC circuit response. In this lab we get large percent error between theoretical and experimental values. It may result from not measuring the data correctly and not correctly inputting the values.