Lab 10 Report

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School

Northeastern University *

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242

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Electrical Engineering

Date

Feb 20, 2024

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pdf

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Lab 10: Inductance PI: Callie Feltner DA: Will Knight Researcher: Grant Wheeler Introduction: Will Knight (DA) In this lab, we tested the practical implications of Faraday's law, which states that a changing magnetic flux through a loop induces a voltage to counteract that change. This phenomenon is mathematically represented by Faraday's law. Notably, this induced voltage is a result of the interplay between a current flowing around a closed circuit, defining a loop, and the creation of a magnetic field within that loop. Through experimentation and analysis, this lab aims to provide understanding of how inductance influences the behavior of circuits Procedure: Grant Wheeler (Researcher) To start out this lab we used the function generator, the oscilloscope, the decade resistance box, the inductor, and the DMM to set up the circuit given to us in the lab manual. The circuit was as shown below: The next thing we did was use the DMM to measure the resistances of each component. We then set the function generator to sin waves with a low frequency and zero offset. We then used the oscilloscope to measure the voltage of the external resistor, called Vr. The measured voltage was then used to calculate the current passing through the whole circuit. We used Ohms Law which states V=IR to find the current. Since we have the resistance value and the voltage (Vr), we used the Ohms Law equation to calculate the current (I). The next step was to record at least 5 low frequency measurements, and 8-10 high frequency measurements. We ended up having 5 low and 9 high. We then used the recorded values to calculate the impedance (Z). Ohms Law was also used here because Δ 𝑉 = ?? . Kirchoff's law was used to prove that the voltage of the generator minus the voltage of the inductor minus the voltage of the external resistor equaled zero. This is because Kirchoff’s Voltage Law states that the sum of all the EMFs in a closed loop is equal to zero.

Researcher 1 : Apply Kirchhoff’s voltage law to your circuit on your low frequency data to calculate the Voltage generated by the function generator. Confirm the Voltage generated by the function generator is constant regardless of frequency. Researcher 2: Explicitly connect the work in PI1, to the high frequency data your group has collected. Explain why “assuming all resistances are zero” is reasonable for your high frequency data. Analysis: Will Knight (DA) DA1: First assess the quality of your raw data. Create two plots of your raw data: a. “Frequency vs. Vr ” b. “Log -Log plot of frequency vs. Vr ” (see Lab 2 for Log -Log plots) DA2 : Return to Lab 4, where Ohm’s Law is defined as Δ 𝑉 = ?? . (3). The inductance of our solenoid must somehow be hiding in the reactance, the imaginary part of Z . Because you have measurements for 𝑉? , the voltage of the power supply, and ? , the current through the power supply, you can directly calculate this ? at all these different frequencies. Create a plot of Frequency vs. ? which best displays your data. (Hint: ? should qualitatively

increase, decrease, or remain constant as you increase the frequency based on Faraday’s Law? Throughout the experiment, the impedance acted as we expected, by increasing with frequency Conclusion: Callie Feltner (PI) PI1: Assume for a moment that all resistances in your circuit are zero. Take advantage of the fact that the current measured in the external resistor was always sinusoidal: ? = ? 0 cos(2 𝜋𝑓𝑡 ) (4) to calculate the maximum induced voltage: 𝜀 𝑚?𝑥 = |− 𝐿 𝑑? / 𝑑𝑡 | 𝑚?𝑥 . (5) Take advantage of the fact that equation (5) can be written in the form of equation (3). The left- hand side is a voltage, and the right-hand side, after some simplification, is a current times some constant (no 𝑡 should survive if you consider the maximum values). The equation for the maximum induced voltage, 𝐸 𝑚𝑎𝑥 = |−𝐿 𝑑𝐼 𝑑𝑡 | , has a close relationship with the equation for the change in voltage, △ 𝑉 = ?? . In this lab, E max is V_G which is 1.75 π . Our 𝐸 𝑚𝑎𝑥 = |−𝐿 𝑑𝐼 𝑑𝑡 | is 0.053(I) * 3.30(z). PI2: Using all the analysis above, calculate 𝐿 . Just to make sure your math is in the correct ballpark; you can be assured that 0.01 ? < 𝐿 < 1 ? . At a low frequency, L causes the voltage and current changes to both be linear due to the resistance values. Using the formula 𝐸 𝑚𝑎𝑥 = |−𝐿 𝑑𝐼 𝑑𝑡 | , I = I 0 *cos(2 πft), and 2πf*I 0 *sin(2πft). Our maximum induced voltages are all around 1.75 V. Using the formula given for inductance, we found ours to be around 0.075 H.

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