1. PHYS 221 Recitation
Kevin Ralphs
Week 8

2. Overview
HW Questions
Alternating Current
RMS
Reactance
Impedance

3. HW Questions
Ask Away…

4. Alternating Current (AC) - RMS
What does it tell me?
RMS is a type of averaging
First square the wave form, then we average and take the square root
Why should I care?
This allows us to keep a form of the Joule heating law
𝑃 𝑎𝑣𝑔 = 𝐼 𝑟𝑚𝑠 2 𝑅

5. AC - Reactance What does it tell me? Why should I care?
Capacitors and inductors resist changes in the state of the circuit – Reactance is a measure of this
Why should I care?
Calculating the voltages on capacitors and inductors in an AC circuit can be complicated
Reactance give you a direct link between the average voltage across these components and the RMS current in an Ohm’s law type format
It also shows how the frequency of the applied voltage affects the system
𝑋 𝐿 =𝜔 𝐿 𝑋 𝐶 = 1 𝜔 𝐶
XL: Inductive Reactance, XC: Capacitive Reactance,
ω = 2πf: Angular frequency, L: Inductance, C: Capacitance

6. AC - Impedance What does it tell me? Why should I care?
It represents the relationship (magnitude and phase difference) between the applied voltage and the current
Why should I care?
You can’t directly add the voltages across different kinds of components because the waves are out of phase
The voltages become like vectors

7. AC - Impedance
Since the impedance carries phase information, it is a complex number
𝑋 𝐿 =𝑖 𝜔 𝐿 𝑋 𝐶 = 1 𝑖 𝜔 𝐶 =− 𝑖 𝜔 𝐶
𝑍=𝑅+ 𝑋 𝐿 + 𝑋 𝐶 =𝑅+𝑖(𝜔𝐿− 1 𝜔 𝐶 )
The circuit is at resonance when the impedance is a real number
This corresponds to maximum power transfer to the resistors