Physics 21: 6-15 Applications of Induction and LRC Circuits

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 21: 6-15

Study Points

21.6 Lenz's law predicts that induced EMF will acti to oppose motion, so when a motor turns, it creates a counter emf or "back emf", which depends on the speed of the motor. This prevents motors from having infinite capacity.
21.7 Since the voltage difference generated in a wire wrapped around a current-carrying coil depends on the number of coils and the magnetic flux through the coil, coil-and-loop systems can be used to step-up (increase) or step-down (decrease) voltage. The relationship of primary (incoming) to secondary (output) voltage depends only on the number of coils in each system: V_S/V_P = N_S/N_P.
21.8 Data can be stored using magnetized materials and semiconductors which are charged/polarized in one direction (ON or "1") or uncharged and unpolarized (OFF or "0"). Sensors read the material as data or instructions to carry out computer processes.
21.9 Induced current varied by sensitive and rapidly moving magnets are used in microphones, magnetic strip readers, and seismographs. Solenoids are also used as fast circuit breakers.
21.10 Mutual inductance occurs when two current-carrying wires are near each other. Changing current in a coil will also induce a back emf in the coil itself (self-inductance).
21.11 As with gravity and electrical fields, energy can be stored in a magnetic field: U = 1/2 * LI².
21.12 A circuit with both inductance and resistance is an LR circuit, which follows exponential laws in its behavior.
21.13 Alternating current driving an LRC circuit follows specific rules as well:
- Resistance varies as voltage (it will be in phase with voltage changes).
- Current will lag voltage by 90° when an inductor is in the circuit.
- Current will lead voltage by 90° when a capacitor is in the circuit.
21.14 Analysis of LRC circuits often involves phasor diagrams, in which voltage drops across each element (V_capacitor, V_resistor, V_inductor) are drawn as independent vectors that can be added using vector math.
21.15 The frequency of the voltage source in an AC circuit will create resonance as a function of the inductance and capacitance in the circuit. Resonance allows TV and radio systems to "tune in" particular frequencies.

Key Equations

The Generator Equation: $ℰ = Bl v_{⊥} = 2 NBlv \sin θ = NB ω A \sin ω t$
Transformer Voltages: $\begin{array}{l} V_{S} = N_{S} \frac{Δ Φ_{B}}{Δ t} \\ V_{P} = N_{P} \frac{Δ Φ_{B}}{Δ t} \end{array}$
Inductance (emf in coil #2 from changing current in coil #1) $ℰ_{2} = - M \frac{Δ I_{1}}{Δ t}$
Energy stored in a magnetic field: $U = ½ L I^{2} = ½ \frac{B^{2}}{μ_{0}} Al where energy density u = ½ \frac{B^{2}}{μ_{0}}$
LR Circuit current $I = \frac{V_{0}}{R} (1 - e^{\frac{- t}{τ}}) where τ = \frac{L}{R}$
Inductive reactance $X_{L} = ω L = 2 π fL$
Capacitive reactance $X_{C} = \frac{1}{ω C} = \frac{1}{2 π fC}$
Average power in LRC circuit: $P = {I_{rms}}^{2} Z \cos φ$
Resonance in AC circuits $f_{0} = \frac{1}{2 π} \sqrt{\frac{1}{LC}}$

Web Lecture

Read the following weblecture before chat: Generators and Transformers

Study Activity

Use the animation at the oPhysics to explore how a simple electrical motor works.

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: Electric Motor (Two week lab)

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Physics

Chapter 21: 6-15 Assignment