Physics 2 Lab 11

.pdf

School

Massachusetts Institute of Technology *

*We aren’t endorsed by this school

Course

8.02

Subject

Electrical Engineering

Date

Oct 30, 2023

Type

pdf

Pages

Uploaded by ElderEchidnaPerson924

RL Circuits Lab Number and Title: 218 RL Circuits Name: Aaron Hsu Group ID: N/A Date of Experiment: 12/6/22 Date of Submission: 12/13/22 Course and Section Number: PHYS 121A013 Instructor’s Name: Matias Daniel de Almeida Partner’s Names: Paul Svorec, Alex Ack, and Noah Francois 1. Introduction: The goals and objectives of this lab are to construct and analyze the current in an RL Circuit. The self induced electromotive force across the inductor is . In an ε ε 𝐿 =− 𝐿 ?𝑖 ?𝑡 RL circuit, if the switch is long enough in any position, the current is constant. If there is no change in current or di/dt=0, the electromotive force across the inductor is 0. The electromotive force which is E exists when the current is changing which means di/dt does not equal 0. In order to change the current in this experiment, we would do this by moving the switch from A to B or from B to A. When the current starts to flow and when the switch is moved to A and with Kirchoff’s Law of voltages the equation is . is the voltage across the battery, R is the resistance in the loop, 𝑉 0 − 𝑖𝑅 − 𝐿 ?𝑖 ?𝑡 = 0 𝑉 0 and L is inductance of the coil. The solution to the previous equation is where is the circuit time constant which is measured 𝑖(𝑡) = ( 𝑉 0 𝑅 )(1 − ? −𝑡/τ ) τ = 𝐿/𝑅 in seconds. Since the voltage across the inductor is the equation is then ε 𝐿 =− 𝐿( ?𝑖 ?𝑡 ) . For the previous equation you can also take the natural logarithm or 𝑉 𝐿 (𝑡) = 𝑉 0 ? −𝑡(𝑅/𝐿) base e of both sides so that the equation becomes which is just a 𝑙𝑛[1 − 𝑖(𝑡) 𝑖 0 ] =− 𝑅 𝐿 𝑡 straight line with slope -R/L and the units of L/R must be in seconds. Once the switch is moved from B to A then current will start to flow but the inductor will generate an EMF such that the current will not flow right away at its full value. The current will actually increase from zero to the max value over time instead. The growth of the current in the

circuit will depend on the inductance and the resistance in the circuit. When the current is stopped and at t<0 with the switch in position A, the current is constant or 𝑖 = 𝑉 0 /𝑅 which then means . When t=0 the switch is moved to position B and ε 𝐿 =− 𝐿 ?𝑖 ?𝑡 = 0 once it is moved to B, Kirchoff’s Law of voltages is where R is the 𝑖𝑅 + 𝐿( ?𝑖 ?𝑡 ) = 0 resistance in the loop and L is the inductance of the coil. The solution to the equation above is where is the circuit time constant measured in 𝑖(𝑡) = ( 𝑉 0 𝑅 )? −𝑡/τ τ = 𝐿/𝑅 seconds. Since the voltage across the inductor is the equation is then ε 𝐿 =− 𝐿( ?𝑖 ?𝑡 ) which you can take the logarithm of both sides which then becomes 𝑉 𝐿 (𝑡) = 𝑉 0 ? −𝑡(𝑅/𝐿) . This is a straight line with slope -R/L and the units must be in 𝑙𝑛[ 𝑖(𝑡) 𝑖 0 ] =− ( 𝑅 𝐿 )𝑡 seconds. When the switch is quickly moved from A to B the current stops the flow but the inductor will generate an EMF so that the current will continue to flow over time. The decrease of the current in the circuit will depend on the inductance and the resistance in the circuit. 2. Experimental Procedure: The equipment that we used for this lab are a digital multimeter, electronic connection board, lab computer with capstone software installed, connection cables or banana cables, voltage probe, LCR meter, 850 universal interface, inductors (current loop and solenoid), and a resistor of 10 ohms. We followed the same procedure as in the lab manual. First we had to set up the RL circuit on the electrical circuit connection board correctly. We did this by making sure the banana cables are connected to the right spots in the interface, the resistor, and the inductor. Then we needed to plug in the voltage probe correctly in the interface and in the resistor. Once we set it up correctly we opened up the lab computer for the software to measure and record our data. Before we clicked on record we first had to use the equations for calculations to calculate the expected time constant. On the measurement page of the lab computer we had to make sure that it is set up correctly with the correct information filled out. Once we have done this, we click record and analyze the graphs by looking at them and getting the slope of the lines and then we