Overview
Instructions
These are the instructions for Lab 9 - LCR. In this lab, an inductor, capacitor, and resistor are placed in series with a sine wave function generator and an ammeter. The ammeter is set to measure the RMS current out of the function generator. The goal of this lab is to numerically integrate the differential equation that describes the current in an LCR series circuit.
[Image unavailable: LaTeX: V_{drive}=V_L+V_C+V_R]Vdrive=VL+VC+VR
[Image unavailable: LaTeX: V_{drive}=L\:\frac{d\:I}{dt}+\frac{Q}{C}+I\:R]Vdrive=LdIdt+QC+IR
Then differentiate with respect to time and reorder the equation
[Image unavailable: LaTeX: L\:\frac{d^2I}{dt^2}+R\:\frac{d\:I}{dt}+\frac{I}{C}=\frac{d}{dt}V_{drive}]Ld2Idt2+RdIdt+IC=ddtVdrive
where [Image unavailable: LaTeX: V_{drive}\left(t\right)=A\:\sin\left(2\pi\:f\:t\right)]Vdrive(t)=Asin?(2?ft)
The goal is to numerically integrate that differential equation in Wolfram Mathematica and then find the relationship between the current through the ammeter, and the drive frequency. Please note, some people refer to this as RCL, RLC, etc; it doesn't matter the order of the components as the results are the same.
Follow these steps:
- Read the Electrical Oscillations: RLC Circuit lab out of the lab manual (page 149).
- Review this topic out of your textbook (College Physics 2nd Edition by Freedman, Ruskell, Kesten, Tauck), page 893.
- Complete the Pre-Lab quiz in Canvas.