PHY 213 Worksheet AC circuits-1-1

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Electrical Engineering

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Jan 9, 2024

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PHY 213 Lab 7 Worksheet: AC circuits PI: DA: Researcher: 1. DA: Include data for Part A & B in legible form in your worksheet. Add appropriate units, etc.

2. DA: Finish the graph for Part A and create a graph for part B, to represent your data.

3. DA: Create captions for the graphs describing the behavior of the data both above and below the “dividing line” mentioned in step 11 for both parts A and B. PART A graph caption: The system’s impedance decreases at a rapid rate below the target frequency, meanwhile the impedance levels out and decreases less rapidly as the system’s frequency increases and approaches close to 10x the target frequency. Part B graph caption: The system’s impedance changes slightly below the target frequency, meanwhile the system’s impedance (rate of change or slope) increases as the frequency increases. 4. Researcher: Use the information found in the Introduction of this Lab to explain the behavior of Z above and below the “dividing line” mentioned in step 11 for Part A.

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Given the information from the introduction of this lab, Z represents the impendence, this is the amount of opposition based by the direct or alternating current when it passes through a conductor component in the circuit. The “dividing line” above and below of Z occurs happens at the resonant frequency of the circuit, above the inductive reactance dominates, while below the captative reactance dominate. For part A, the higher the frequency goes, the lower the impendence goes (Z). 5. Researcher: Use the information found in the Introduction of this Lab to explain the behavior of Z above and below the “dividing line” mentioned in step 11 for part B. Z represents the impendence; this is the amount of opposition based by the direct or alternating current when it passes through a conductor component in the circuit. For part B, the higher the frequency goes, the higher the impendence goes. 6. Researcher: Explain how the voltage divider formula was derived and used. Specifically, if Ohm’s Law is NOT ΔV = IR , then how can we use it in the prelab to derive the voltage divider formula? V total Z total = V R R The voltage divider formula was derived from a circuit with two different resistors, where the output voltage is equal to the input voltage multiplied by the fraction of the second resistor divided by the total resistance of the circuit. This is an electrical circuit whose output is smaller than the input. When ohm’s law is V- I/R instead of V=iR, that is when we arrive to the voltage divider formula. 7. PI: There should be multiple spots in the data where Z≈ R . In each of these cases, Z − R is approximately constant for each part. Explain this systematic uncertainty in terms of the rest of the equipment involved. Feel free to use the DMM to help you find this missing resistance. There are multiple impedance (Z) values in the RL and RC circuit that match the resistance. In the RL circuit, the impedance was initially around the value of the resistance and increased as the frequency increased. In the RC circuit, the impedance started off at a higher value and decreased until it leveled off at the resistance value. The systematic uncertainty could have been due to the equipment used to measure the voltage. Since the oscilloscope was used to measure the total voltage and the voltage drop of the resistor, there could have been slight misreadings each time the voltage was recorded. Since the impedance was determined by using the voltage divider formula, this could have affected the impedance values.

8. PI: What is the significance of f target ? Specifically, why does the behavior of Z change at approximately this frequency? Can you use this information to find the precise formula for X C and X L ? (Feel free to search the internet for the formulae for X C and X L and work through these questions in reverse order). The target frequency is the frequency at which the impedance accurately reflects the behavior of the RL or RC circuit. f target is also the frequency at which the impedance will approximately equal the resistance R. Using the formula for impedance Z = √ R 2 +( X L − X C ) 2 , and knowing X C 1 f and X L f , the reactance of each should cancel out at approximately the target frequency and lead to Z = R. Using the resonance frequency formula, f = 1 2 π √ LC , we can find X c and X L by plugging in our known falues (f and either L or C), and we get the equations X L = 2 Π fL and X C = 1 2 Π fC . 9. PI: The RC and RL circuit combinations we studied today are vital within electronics because they can be used to create “ High-pass ” and “ Low-pass” filters . Do a bit of research on these two types of circuits and explain how your groups results relate to these important pieces of technology. Specifically, how does the behavior of Z as a function of frequency allow these RC or RL circuits to filter out either high frequency or low frequency noise? The RC circuit would be considered a low pass filter because it allows low frequencies to pass through the circuit. From the data in the RC circuit, the impedance decreases until it reaches the target frequency and remains constant. This implies that this circuit will allow frequencies below the “cut off” frequency to pass through, while blocking high frequency noises. The RL circuit is a high pass filter, as it allows high frequencies to pass through the circuit. The impedance stayed relatively constant until the target frequency was approaching, and it increased significantly just 2 or 3 trials before the end. This implies that higher frequencies than the cut off frequency will continue to pass through the circuit, while attenuating low frequency noise.