Physics 18: 7-10 Alternating Current

Homework

Reading Preparation
Key Equations
WebLecture
Study Activity
Chat Preparation Activities
Chapter Quiz
Lab Work

Reading Preparation

Text Reading: Giancoli, Physics - Principles with Applications, Chapter 18: Sections 7 to 10

Study Points

18.7 Alternating current sources cycle the direction in which the current flows. Voltage amplitude varies with time as a sine wave, V = V₀sin 2πft. Again, we can substitute this into expressions for I = V/R and P = I²R. Over time between maximum and minimum, sin (any angle) fluctuates between 0 and 1, so the average of any of these will be 1/2 the maximum based on V₀: P_average = 1/2 (V₀²)/R. The value V_{root mean square} = sqrt (1/2 V₀²).
18.8 While electrons may have high speeds, they do not move consistently in one direction along a wire but collide with stationary atoms and each other. As a result, their net forward motion or drift velocity is less than their actual speed. I = ΔQΔt = neAv_d.
18.9 At low temperatures, stationary molecules vibrate less, and the number of collisions for moving electrons becomes less (resistance decreases). Drift velocity increases so that the net result is a kind of superconductivity.
18.10 The human nervous system is an electrical network. Signals occur when the potential difference across a neuron membrane climbs above a minimum limit (the action potential) and triggers a chemical reaction that carries the charge along the surface of the cell, or between the segments of an axon.

Key Equations

Alternating current voltage, current, and power: $\begin{array}{l} V = V_{0} \sin 2 π ft = V_{0} \sin ω t \\ I = I_{0} \sin ω t \\ P = {I_{0}}^{2} R \sin^{2} ω t \end{array}$
Average values (root mean square values): $If x = \sin^{2} ω t, x_{avg} = ½ .$
$P = {I_{0}}^{2} R \sin^{2} ω t \Rightarrow P_{avg} = {½ I}_{0}^{2} R$
$x_{rms} = \sqrt{(x_{avg})^{2}}$ $P = I_{rms} V_{rms} = {½ I}_{0}^{2} R = {I_{rms}}^{2} R = \frac{{½ V}_{0}^{2}}{R} = \frac{{V_{rms}}^{2}}{R}$

Web Lecture

Read the following weblecture before chat: Alternating Current and Electrical Power

Study Activity

Use a graphic calculator, a tool such as Mac's Grapher, such as the one at Desmos.

Enter an equation in the form y = sin 2πt and graph it. This is essentially the same as V = V₀ sine 2πf₀t, when V₀ = 1 and f₀ = 1.
Now vary the equation by adding a different period, instead of 2 πt, enter 2 π2t. What happens?
Now vary the equation by adding a different period, instead of 2 πt, enter 2 π(1/2)t. What happens?
Now vary the equation by adding a different maximum value for V₀, such as 2 or 3. What happens?
How does changing the maximum voltage on an AC circuit change the behavior of current on the circuit?
How does changing the oscillation period on the AC circuit change the behavior of the circuit?

Chat Preparation Activities

Forum question: The Moodle forum for the session will assign a specific study question for you to prepare for chat. You need to read this question and post your answer before chat starts for this session.
Mastery Exercise: The Moodle Mastery exercise for the chapter will contain sections related to our chat topic. Try to complete these before the chat starts, so that you can ask questions.

Chapter Quiz

Required: Complete the Mastery exercise with a passing score of 85% or better.
Go to the Moodle and take the quiz for this chat session to see how much you already know about astronomy!

Lab Work

If you want lab credit for this course, you must complete at least 18 labs; you may complete more if you are preparing for the AP exam.. One or more lab exercises are posted for each chapter as part of the homework assignment. We will be reviewing lab work at regular intervals, so do not get behind!

Lab Instructions: Internal Resistance of a Battery

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Physics

Chapter 18: 7-10 Assignment