Lecture 19-1 RL Circuits – Starting Current 2. Loop Rule: 3. Solve this differential equation τ=L/R is the inductive time constant 1.Switch to e at t=0 As the current tries to begin flowing, self-inductance induces back EMF, thus opposing the increase of I. + - ε/R

Lecture 19-2 Alternating Current (AC) = Electric current that changes direction periodically ac generator is a device which creates an ac emf/current. ac motor = ac generator run in “reverse” A sinusoidally oscillating EMF is induced in a loop of wire that rotates in a uniform magnetic field. where

Lecture 19-3 ©2008 by W.H. Freeman and Company

Lecture 19-4 READING QUIZ 1 \ Which of the following statements is correct ? A| In A.C. circuit with a A.C. generator and an ideal capacitor the current lags the voltage. B| In an A.C. circuit with a A.C. generator and an ideal inductor the current leads the voltage. C| In an circuit consists of an ideal inductor and an ideal capacitor. The capacitor is initially charged. After the switch is thrown energy is dissipated every cycle. D| In an A.C. circuit consists of an ideal inductor, an ideal capacitor and a series resistor. Initially the capacitor is charged After the switch is thrown energy is dissipated.

Lecture 19-5 Resistive Load Start by considering simple circuits with one element (R, C, or L) in addition to the driving emf. Pick a resistor R first. v R (t) and I(t) in phase Kirchhoff’s Loop Rule: I peak + -- I(t)

Lecture 19-6 ©2008 by W.H. Freeman and Company

Lecture 19-7 Power Dissipated by Resistive Load V R and I in phase Power:

Lecture 19-8 Average Power but

Lecture 19-9 Root-Mean-Square Values Similarly,

Lecture Capacitive Load I(t) leads v(t) by 90 o (1/4 cycle) Loop Rule: Power: +--

Lecture ©2008 by W.H. Freeman and Company

Lecture Inductive Load I(t) lags v(t) by 90 o (1/4 cycle) Kirchhoff’s Loop Rule: Power: +--

Lecture ©2008 by W.H. Freeman and Company

Lecture Capacitive vs Inductive Load I(t) leads v(t) by 90 o capacitive reactance v L (t) leads I(t) by 90 o inductive reactance vLvL

Lecture WARM UP QUIZ 2 Which of the following statements is correct? A. B. C. D.

Lecture ENERGY STORED IN AN INDUCTOR 6C07

Lecture (Ideal) LC Circuit From Kirchhoff’s Loop Rule From Energy Conservation same Natural Frequency harmonic oscillator with angular frequency

Lecture ©2008 by W.H. Freeman and Company

Lecture RC Circuit vs LC Circuit RC +Q -Q I convention so that t I 0 -Q/(CR) t 0 -I max I max In RC circuit, current I causes energy dissipation in resistor R. exponential decay In LC circuit, there is no energy dissipation – energy can be stored in L, C, or both. sinusoidal oscillation

Lecture ©2008 by W.H. Freeman and Company

Lecture ©2008 by W.H. Freeman and Company

Lecture DEMO DAMPED OSCILLATIONS 6C10

Lecture LC Oscillations No Resistance = No dissipation

Lecture PHYSICS 241 NOVEMBER 1, :30 QUIZ 3 In most of Europe, the rms voltage of household outlets is 220V. What is the peak voltage? a) 110V b) 141V c) 156V d) 220V e) 311V

Lecture PHYSICS 241 NOVEMBER 1, :30 QUIZ 3 In most of Europe, the peak voltage of household outlets is 311V. What is the rms voltage? a) 110V b) 141V c) 156V d) 220V e) 311V

Lecture PHYSICS 241 –MARCH 24, 2011 QUIZ 3 In Japan, the rms voltage of household outlets is 100V. What is the peak voltage? a) 200V b) 141V c) 100V d) 50V e) 71V