# PHYS 212 Study Guide - Midterm Guide: Virtual Image, Refraction, Plane Wave

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Published on 19 Apr 2015
School
University of Illinois
Department
Physics
Course
PHYS 212
Professor
PHYS 212- Spring 2014
Exam #3- Review Sheet
Questions & Corrections: Hassan Shapourian (hassan88@illinois.edu)
General tip
Be careful about units. Often prefixes are used as there are small or large quantities. Always convert
prefixes back to the base unit before using them mathematically. Sometimes you can find the correct
choice by checking the signs/dimensions/limiting behavior.
LC Circuits
Oscillator circuit with energy  

. Think about as “position” and as “velocity” then this expression
looks like energy of a Harmonic oscillator with mass    and spring constant  . Hence, the oscillation
frequency is
.
If we add a resistor to the circuit, if there is no external EMF, it will consume energy and after a long time both
capacitor and inductor will be discharged.
AC Circuits and Phasors
An RLC circuit is driven by a sinusoidal voltage source   . We are interested in steady state
behavior at which the current through circuit is  . Note that what matters here is the phase
difference between and ; i.e. you can put the relative phase in current:    and so
 .
The voltage-current relations are given by
Reactances and (in units of ohm) play the role of effective resistance very similar to the expression for
resistors   . Use the mnemonic “ELI-the-ICEman” for remembering the phase rules: “EMF leads I across L,
and I leads EMF across C”.
Phasors
Each oscillating quantity    is represented by a vector the projection of which on vertical
axis gives . The length of a phasor is the peak value  and the angle with positive horizontal axis is the initial
phase . The phasor rotates counterclockwise with time around the origin. When quantity A has a larger angle
(phase) than quantity B, we say A leads B by .
E leads I E lags I E and I are in-phase (resonance case)
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