Class 14 - BYU Physics and Astronomy
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Class 14 Physics 106 Learning Outcomes Class 14 AC Circuits and Electromagnetic Waves Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Physics 106 Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Press CTRL-L to view as a slide show. Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Learning Outcomes Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Last time we discussed: Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Learning Outcomes Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Last time we discussed: I Inductors and self-inductance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Learning Outcomes Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Last time we discussed: I Inductors and self-inductance I RL Circuit Problems Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Learning Outcomes Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Last time we discussed: I Inductors and self-inductance I RL Circuit Problems I AC Circuit Terminology Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Learning Outcomes Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Last time we discussed: Power in AC Circuits I Inductors and self-inductance I RL Circuit Problems I AC Circuit Terminology Transformers I R, L, and C in AC Circuits Maxwell’s Ideas An AC Circuit Problem Resonance Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Learning Outcomes Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Today we will discuss: Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Learning Outcomes Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Today we will discuss: I The Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Learning Outcomes Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Today we will discuss: I The Series RLC Circuit I Power in AC Circuits Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Learning Outcomes Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Today we will discuss: I The Series RLC Circuit I Power in AC Circuits I Resonance Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Learning Outcomes Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Today we will discuss: I The Series RLC Circuit I Power in AC Circuits I Resonance I Transformers Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Learning Outcomes Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Today we will discuss: I The Series RLC Circuit I Power in AC Circuits I Resonance I Transformers I Radiation Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Phasors and the Series RLC Circuit Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light The RLC Series Circuit Class 14 Physics 106 Learning Outcomes I I The resistor, inductor, and capacitor can be combined in a circuit The current in the circuit is the same at any time and varies sinusoidally with time Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light The RLC Series Circuit Class 14 Physics 106 Learning Outcomes I I The resistor, inductor, and capacitor can be combined in a circuit The current in the circuit is the same at any time and varies sinusoidally with time Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Current and Voltage Relationships in an RLC Circuit Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I In a series RLC circuit, the voltages across the R, L, and C must add to equal the voltage of the power supply at all times. Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Phasor Diagram for RLC Series Circuit Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I Let I = Imax sin(2πft). Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Phasor Diagram for RLC Series Circuit Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I Let I = Imax sin(2πft). I At time t = 0, the current is 0. Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Phasor Diagram for RLC Series Circuit Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I Let I = Imax sin(2πft). I At time t = 0, the current is 0. I At time t = 0, the current phasor is in the x direction. Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Phasor Diagram for RLC Series Circuit Class 14 Physics 106 I I I The voltage across the resistor is on the +x axis since it is in phase with the current The voltage across the inductor is on the +y axis since it leads the current by 90◦ The voltage across the capacitor is on the −y axis since it lags behind the current by 90◦ Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Phasor Diagram for RLC Series Circuit Class 14 Physics 106 I I I The voltage across the resistor is on the +x axis since it is in phase with the current The voltage across the inductor is on the +y axis since it leads the current by 90◦ The voltage across the capacitor is on the −y axis since it lags behind the current by 90◦ Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Phasor Diagram for RLC Series Circuit Class 14 Physics 106 I I I The voltage across the resistor is on the +x axis since it is in phase with the current The voltage across the inductor is on the +y axis since it leads the current by 90◦ The voltage across the capacitor is on the −y axis since it lags behind the current by 90◦ Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Circuit Rules for AC Circuits Class 14 Physics 106 Learning Outcomes If two or more circuit elements are in series, they have the same current phasor: Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Phasor Diagram for RLC Series Circuit Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits I Add voltage phasors (as vectors) to get the total emf An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Impedance and Phasors Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I Divide voltages by the current Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Impedance and Phasors Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I Divide voltages by the current I Z is the "impedance" Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Impedance and Phasors Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I Divide voltages by the current I Z is the "impedance" I Vmax = Imax Z Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Impedance and Ohm’s Law Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I Ohm’s Law can be applied to the impedance I Vmax = Imax Z I This can be regarded as a generalized form of Ohm’s Law applied to a series AC circuit Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Impedance and Ohm’s Law Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I Ohm’s Law can be applied to the impedance I Vmax = Imax Z I This can be regarded as a generalized form of Ohm’s Law applied to a series AC circuit Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Impedance and Ohm’s Law Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I Ohm’s Law can be applied to the impedance I Vmax = Imax Z I This can be regarded as a generalized form of Ohm’s Law applied to a series AC circuit Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Summary of Circuit Elements, Impedance and Phase Angles Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Power in an AC Circuit Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I No power lost in C or L Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Power in an AC Circuit Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I No power lost in C or L I Energy is stored in these fields and drawn back out of fields Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Power in an AC Circuit Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I No power lost in C or L I Energy is stored in these fields and drawn back out of fields I Power is only lost in R Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Power in an AC Circuit Class 14 Physics 106 Learning Outcomes I Average Power Phasors and the Series RLC Circuit Impedance Loss: Pav = Irms VR,rms = Irms Vsource,rms cos φ Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Power in an AC Circuit Class 14 Physics 106 Learning Outcomes I Average Power Phasors and the Series RLC Circuit Impedance Loss: Pav = Irms VR,rms = Irms Vsource,rms cos φ Power in AC Circuits An AC Circuit Problem Resonance Transformers I cos φ is called the power factor of the circuit Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance An AC Circuit Problem Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light A Series RLC Circuit Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance A series RLC circuit consists of I 120 Vrms, 60.0 Hz power supply I 5.00 Ω resistor I 200 µF capacitor I 12.0 mH inductor Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light A Series RLC Circuit Class 14 Physics 106 A series RLC circuit consists of I 120 Vrms, 60.0 Hz power supply I 5.00 Ω resistor I 200 µF capacitor I 12.0 mH inductor Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light A Series RLC Circuit Class 14 Physics 106 A series RLC circuit consists of I 120 Vrms, 60.0 Hz power supply I 5.00 Ω resistor I 200 µF capacitor I 12.0 mH inductor I What are XL , XC , and Z ? Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Class 14 A Series RLC Circuit Physics 106 A series RLC circuit consists of I 120 Vrms, 60.0 Hz power supply I 5.00 Ω resistor I 200 µF capacitor I 12.0 mH inductor I What are XL , XC , and Z ? XL = 2πfL = 4.52Ω Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance 1 XC = = 13.3Ω 2πfC Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Class 14 A Series RLC Circuit Physics 106 A series RLC circuit consists of I 120 Vrms, 60.0 Hz power supply I 5.00 Ω resistor I 200 µF capacitor I 12.0 mH inductor I What are XL , XC , and Z ? XL = 2πfL = 4.52Ω Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance 1 XC = = 13.3Ω 2πfC q Z = R 2 + (XL − XC )2 = 10.1Ω Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light A Series RLC Circuit Class 14 Physics 106 Learning Outcomes A series RLC circuit consists of I 120 Vrms, 60.0 Hz power supply I 5.00 Ω resistor I 200 µF capacitor I 12.0 mH inductor I Draw a phasor diagram for the impedance. Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light A Series RLC Circuit Class 14 Physics 106 Learning Outcomes A series RLC circuit consists of I 120 Vrms, 60.0 Hz power supply I 5.00 Ω resistor I 200 µF capacitor I 12.0 mH inductor I Draw a phasor diagram for the impedance. Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light A Series RLC Circuit A series RLC circuit consists of Class 14 Physics 106 Learning Outcomes I 120 Vrms, 60.0 Hz power supply Phasors and the Series RLC Circuit I 5.00 Ω resistor Power in AC Circuits I 200 µF capacitor I 12.0 mH inductor I Find the phase angle, φ, between the power supply and the current. Impedance An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light A Series RLC Circuit A series RLC circuit consists of Class 14 Physics 106 Learning Outcomes I 120 Vrms, 60.0 Hz power supply Phasors and the Series RLC Circuit I 5.00 Ω resistor Power in AC Circuits I 200 µF capacitor I 12.0 mH inductor I Find the phase angle, φ, between the power supply and the current. XL − XC R φ = −60.2◦ φ = tan−1 Impedance An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light A Series RLC Circuit Class 14 Physics 106 A series RLC circuit consists of I 120 Vrms, 60.0 Hz power supply I 5.00 Ω resistor I 200 µF capacitor I 12.0 mH inductor I What are Irms and Imax ? Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light A Series RLC Circuit Class 14 Physics 106 A series RLC circuit consists of I 120 Vrms, 60.0 Hz power supply I 5.00 Ω resistor Phasors and the Series RLC Circuit Impedance I 200 µF capacitor I 12.0 mH inductor I What are Irms and Imax ? Irms Learning Outcomes Vrms = = 11.9A Z Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light A Series RLC Circuit Class 14 Physics 106 A series RLC circuit consists of I 120 Vrms, 60.0 Hz power supply I 5.00 Ω resistor I 200 µF capacitor I 12.0 mH inductor I What are Irms and Imax ? Vrms Irms = = 11.9A Z √ Imax = 2Irms = 16.9A Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light A Series RLC Circuit Class 14 Physics 106 A series RLC circuit consists of I 120 Vrms, 60.0 Hz power supply I 5.00 Ω resistor I 200 µF capacitor I 12.0 mH inductor I What are the maximum voltages across each circuit element? Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light A Series RLC Circuit Class 14 Physics 106 A series RLC circuit consists of I 120 Vrms, 60.0 Hz power supply I 5.00 Ω resistor I 200 µF capacitor I 12.0 mH inductor Learning Outcomes Phasors and the Series RLC Circuit Impedance What are the maximum voltages across each circuit element? √ Vs,max = 120 2 = 170V I Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light A Series RLC Circuit Class 14 Physics 106 A series RLC circuit consists of I 120 Vrms, 60.0 Hz power supply I 5.00 Ω resistor I 200 µF capacitor I 12.0 mH inductor Learning Outcomes Phasors and the Series RLC Circuit Impedance What are the maximum voltages across each circuit element? √ Vs,max = 120 2 = 170V VR,max = Imax R = 84.3V I Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light A Series RLC Circuit Class 14 Physics 106 A series RLC circuit consists of I 120 Vrms, 60.0 Hz power supply I 5.00 Ω resistor I 200 µF capacitor I 12.0 mH inductor Learning Outcomes Phasors and the Series RLC Circuit Impedance What are the maximum voltages across each circuit element? √ Vs,max = 120 2 = 170V VR,max = Imax R = 84.3V I Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits VL,max = Imax XL = 76.2V Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light A Series RLC Circuit Class 14 Physics 106 A series RLC circuit consists of I 120 Vrms, 60.0 Hz power supply I 5.00 Ω resistor I 200 µF capacitor I 12.0 mH inductor Learning Outcomes Phasors and the Series RLC Circuit Impedance What are the maximum voltages across each circuit element? √ Vs,max = 120 2 = 170V VR,max = Imax R = 84.3V I Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits VL,max = Imax XL = 76.2V VC,max = Imax XC = 224V Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light A Series RLC Circuit Class 14 Physics 106 A series RLC circuit consists of I 120 Vrms, 60.0 Hz power supply I 5.00 Ω resistor I 200 µF capacitor I 12.0 mH inductor Learning Outcomes Phasors and the Series RLC Circuit Impedance What are the maximum voltages across each circuit element? √ Vs,max = 120 2 = 170V VR,max = Imax R = 84.3V I Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits VL,max = Imax XL = 76.2V VC,max = Imax XC = 224V Vs,max = Imax Z = 170V Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light A General Expression for the Voltage Class 14 Physics 106 Learning Outcomes I We may write the current in a series RLC circuit as Phasors and the Series RLC Circuit Impedance I(t) = Imax sin(2πft) Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light A General Expression for the Voltage Class 14 Physics 106 Learning Outcomes I We may write the current in a series RLC circuit as Phasors and the Series RLC Circuit Impedance I(t) = Imax sin(2πft) Power in AC Circuits An AC Circuit Problem Resonance I The voltage across a circuit element is V (t) = Vmax sin(2πft + φ) Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Voltages in the Circuit Class 14 Physics 106 I The voltage across the resistor is VR (t) = VR,max sin(2πft + 0◦ ) Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Class 14 Voltages in the Circuit Physics 106 I The voltage across the resistor is Learning Outcomes VR (t) = VR,max sin(2πft + 0◦ ) Phasors and the Series RLC Circuit Impedance Power in AC Circuits I An AC Circuit Problem The voltage across the inductor is ◦ VL (t) = VL,max sin(2πft + 90 ) Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Class 14 Voltages in the Circuit Physics 106 I The voltage across the resistor is Learning Outcomes VR (t) = VR,max sin(2πft + 0◦ ) Phasors and the Series RLC Circuit Impedance Power in AC Circuits I An AC Circuit Problem The voltage across the inductor is ◦ VL (t) = VL,max sin(2πft + 90 ) Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits I The voltage across the capacitor is VC (t) = VC,max sin(2πft − 90◦ ) Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Voltages in the Circuit Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits The current is the red line. An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Voltages in the Circuit Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits I The voltage across the power supply is V (t) = Vmax sin(2πft + φ) An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Voltages in the Circuit Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Voltages in the Circuit Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Resonance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Resonance in an AC Circuit Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I Fix R, L, and C Power in AC Circuits I Fix Vmax An AC Circuit Problem I Steadily increase f and see what happens to I(t) Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Resonance in an AC Circuit Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I Fix R, L, and C Power in AC Circuits I Fix Vmax An AC Circuit Problem I Steadily increase f and see what happens to I(t) Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Resonance in an AC Circuit Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I Fix R, L, and C Power in AC Circuits I Fix Vmax An AC Circuit Problem I Steadily increase f and see what happens to I(t) Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Resonance in an AC Circuit Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I Fix R, L, and C Power in AC Circuits I Fix Vmax An AC Circuit Problem I Steadily increase f and see what happens to I(t) Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Resonance in an AC Circuit Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I Next, plot Irms as a function of frequency Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Resonance in an AC Circuit Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I I Next, plot Irms as a function of frequency Irms is a maximum at the "resonant frequency," f0 Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Resonance in an AC Circuit Class 14 Physics 106 Vrms Z Vrms Irms = =p R 2 + (XL − XC )2 Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Resonance in an AC Circuit Class 14 Physics 106 Vrms Z Vrms Irms = =p R 2 + (XL − XC )2 This is a maximum when Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers XL = XC Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Resonance in an AC Circuit Class 14 Physics 106 Vrms Z Vrms Irms = =p R 2 + (XL − XC )2 This is a maximum when Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers XL = XC Maxwell’s Ideas Hertz and LC Circuits 2πf0 L = 1 2πf0 C Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Class 14 Resonance in an AC Circuit Physics 106 Learning Outcomes Vrms Z Vrms Irms = Phasors and the Series RLC Circuit Impedance =p R 2 + (XL − XC )2 Power in AC Circuits An AC Circuit Problem This is a maximum when Resonance Transformers XL = XC Maxwell’s Ideas Hertz and LC Circuits 2πf0 L = 1 2πf0 C f0 = 1 √ 2π LC Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Transformers Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Transformers Class 14 Physics 106 Learning Outcomes I A transformer is made of two coils of wire wound around a core of soft iron Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Transformers Class 14 Physics 106 Learning Outcomes I I A transformer is made of two coils of wire wound around a core of soft iron The input side connected is the primary and has N1 turns Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Transformers Class 14 Physics 106 I The other side is the secondary and has N2 turns Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Transformers Class 14 Physics 106 I I The other side is the secondary and has N2 turns The iron increases the magnetic flux and keeps the field lines inside the core Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Transformers Class 14 Physics 106 I I I The other side is the secondary and has N2 turns The iron increases the magnetic flux and keeps the field lines inside the core The rate of change of the flux is the same for both coils Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Class 14 Transformers Physics 106 Learning Outcomes Phasors and the Series RLC Circuit I The voltages are related by V2 N2 = V1 N1 Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Class 14 Transformers Physics 106 Learning Outcomes Phasors and the Series RLC Circuit I The voltages are related by V2 N2 = V1 N1 Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas I If N2 > N1 it is a step up transformer Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Class 14 Transformers Physics 106 Learning Outcomes Phasors and the Series RLC Circuit I The voltages are related by V2 N2 = V1 N1 Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas I If N2 > N1 it is a step up transformer I If N2 < N1 it is a step down transformer Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Transformers Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit I The power input into the primary equals the power output at the secondary Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Transformers Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit I I The power input into the primary equals the power output at the secondary Power in AC Circuits I1 V1 = I2 V2 An AC Circuit Problem (Big V means small I) Impedance Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Transformers Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit The power input into the primary equals the power output at the secondary Power in AC Circuits I I1 V1 = I2 V2 An AC Circuit Problem I This assumes an ideal transformer with a resistive load I (Big V means small I) Impedance Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Transformers Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit The power input into the primary equals the power output at the secondary Power in AC Circuits I I1 V1 = I2 V2 An AC Circuit Problem I This assumes an ideal transformer with a resistive load Resonance In real transformers, power efficiencies typically range from 90% to 99% Maxwell’s Ideas I I (Big V means small I) Impedance Transformers Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Maxwell’s Ideas Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light James Clerk Maxwell Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light James Clerk Maxwell Class 14 Physics 106 I 1831 -1879 Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light James Clerk Maxwell Class 14 Physics 106 I 1831 -1879 I Electricity and magnetism were originally thought to be unrelated Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light James Clerk Maxwell Class 14 Physics 106 I 1831 -1879 I Electricity and magnetism were originally thought to be unrelated I in 1865, James Clerk Maxwell provided a mathematical theory that showed a close relationship between all electric and magnetic phenomena Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Maxwell’s Starting Points Class 14 Physics 106 Learning Outcomes I I I Maxwell began with the idea of electric and magnetic field lines He developed a model of the "aether" that provided a mechanical explanation for field lines. The model consisted of "vortices" and "idle wheels." Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Maxwell’s Starting Points Class 14 Physics 106 Learning Outcomes I I I Maxwell began with the idea of electric and magnetic field lines He developed a model of the "aether" that provided a mechanical explanation for field lines. The model consisted of "vortices" and "idle wheels." Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Maxwell’s Starting Points Class 14 Physics 106 Learning Outcomes I I I Maxwell began with the idea of electric and magnetic field lines He developed a model of the "aether" that provided a mechanical explanation for field lines. The model consisted of "vortices" and "idle wheels." Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Maxwell’s Starting Points Class 14 Physics 106 Learning Outcomes I I I Maxwell began with the idea of electric and magnetic field lines He developed a model of the "aether" that provided a mechanical explanation for field lines. The model consisted of "vortices" and "idle wheels." Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Maxwell’s Model Class 14 Physics 106 I Electric charge causes the aether to expand or contract, causing forces on other charges. This made E field lines. Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Maxwell’s Model Class 14 Physics 106 Learning Outcomes I Moving charges caused the vortices to rotate and the idle wheels to counter-rotate. This made B field lines. Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Maxwell’s Predictions Class 14 Physics 106 Learning Outcomes I Maxwell used his model to demonstrate that changing electric fields should "produce" magnetic fields, just as changing magnetic fields "produce" electric fields. Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Maxwell’s Predictions Class 14 Physics 106 Learning Outcomes I I Maxwell used his model to demonstrate that changing electric fields should "produce" magnetic fields, just as changing magnetic fields "produce" electric fields. This led to a wave equation for the fields. The waves were predicted to move with the speed v = √10 µ0 = 3 × 108 m/s Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Maxwell’s Predictions Class 14 Physics 106 Learning Outcomes I I I Maxwell used his model to demonstrate that changing electric fields should "produce" magnetic fields, just as changing magnetic fields "produce" electric fields. This led to a wave equation for the fields. The waves were predicted to move with the speed v = √10 µ0 = 3 × 108 m/s He concluded that visible light and all other electromagnetic waves consist of fluctuating electric and magnetic fields, with each varying field inducing the other Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Hertz and LC Circuits Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Hertz’s Confirmation of Maxwell’s Predictions Class 14 Physics 106 Learning Outcomes I 1857 -1894 I First to generate and detect electromagnetic waves in a laboratory setting I I Showed radio waves could be reflected, refracted and diffracted The unit Hz is named for him Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Hertz’s Basic LC Circuit Class 14 Physics 106 Learning Outcomes I When the switch is closed, oscillations occur in the current and in the charge on the capacitor Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Hertz’s Basic LC Circuit Class 14 Physics 106 Learning Outcomes I When the switch is closed, oscillations occur in the current and in the charge on the capacitor Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance I When the capacitor is fully charged, the total energy of the circuit is stored in the electric field of the capacitor Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light LC Circuits Class 14 Physics 106 Learning Outcomes I An LC circuit consists of an inductor and a capacitor. Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light LC Circuits Class 14 Physics 106 I Initially the capacitor is charged. Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light LC Circuits Class 14 Physics 106 I Initially the capacitor is charged. I No current flows as the inductor initially prevents it. Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light LC Circuits Class 14 Physics 106 I Initially the capacitor is charged. I No current flows as the inductor initially prevents it. I Energy is in the electric field of the capacitor. Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light LC Circuits Class 14 Physics 106 I The charge reduces. Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light LC Circuits Class 14 Physics 106 I The charge reduces. I Current increases. Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light LC Circuits Class 14 Physics 106 I The charge reduces. I Current increases. I Energy is shared by the capacitor and the inductor. Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light LC Circuits Class 14 Physics 106 I The charge goes to zero. Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light LC Circuits Class 14 Physics 106 I The charge goes to zero. I Current increases to a maximum value. Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light LC Circuits Class 14 Physics 106 I The charge goes to zero. I Current increases to a maximum value. I Energy is in the magnetic field of the inductor. Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light LC Circuits Class 14 Physics 106 I The inductor keeps current flowing. Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light LC Circuits Class 14 Physics 106 I The inductor keeps current flowing. I The capacitor begins charging the opposite way. Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light LC Circuits Class 14 Physics 106 I The inductor keeps current flowing. I The capacitor begins charging the opposite way. I The capacitor and inductor share the energy. Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light LC Circuits Class 14 Physics 106 I The capacitor becomes fully charged. Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light LC Circuits Class 14 Physics 106 I The capacitor becomes fully charged. I Current stops. Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light LC Circuits Class 14 Physics 106 I The capacitor becomes fully charged. I Current stops. I All the energy is in the capacitor. Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light LC Circuits Class 14 Physics 106 I The capacitor begins to discharge. Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light LC Circuits Class 14 Physics 106 I The capacitor begins to discharge. I Current flows counterclockwise. Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light LC Circuits Class 14 Physics 106 I The capacitor begins to discharge. I Current flows counterclockwise. I The capacitor and inductor share the energy. Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light LC Circuits Class 14 Physics 106 Learning Outcomes I Without energy loss, current would continue to oscillate forever. Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Class 14 Oscillating Frequency Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I The frequency of oscillation is the same as the resonant frequency of the same L and C in a series RLC circuit. f0 = 1 √ 2π LC Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Electromagnetic Radiation Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light The Fields of Accelerating Charges Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit I Moving charges produce both electric and magnetic fields Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light The Fields of Accelerating Charges Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit I I Moving charges produce both electric and magnetic fields Acceleration fields are "doglegs" in field lines produced when charges accelerate. Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light The Fields of Accelerating Charges Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit I Moving charges produce both electric and magnetic fields Impedance Power in AC Circuits I Acceleration fields are "doglegs" in field lines produced when charges accelerate. An AC Circuit Problem I Acceleration fields become perpendicular to the direction the filed moves. Transformers Resonance Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light The Fields of Accelerating Charges Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit I Moving charges produce both electric and magnetic fields Impedance Power in AC Circuits I Acceleration fields are "doglegs" in field lines produced when charges accelerate. An AC Circuit Problem I Acceleration fields become perpendicular to the direction the filed moves. Transformers Acceleration fields fall off as 1/r rather than 1/r 2 . Hertz and LC Circuits I Resonance Maxwell’s Ideas Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Electric Fields of Accelerating Charges Class 14 Physics 106 I A charge is initially at rest. It accelerates to the right until it goes 70% of the speed of light. Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Electric Fields of Accelerating Charges Class 14 Physics 106 I A charge accelerates to 70% of the speed of light and then is then stopped. Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Electric Fields of Accelerating Charges Class 14 Physics 106 Learning Outcomes I A charge oscillates along the xaxis. Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Electric Fields of Accelerating Charges Class 14 Physics 106 I A 3D view of the same thing with segments of field lines. Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Properties of Electromagnetic Radiation Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Charges and Fields Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I Stationary charges produce only electric fields Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Charges and Fields Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I Stationary charges produce only electric fields Power in AC Circuits I Charges in uniform motion (constant velocity) produce electric and magnetic fields An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Charges and Fields Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I Stationary charges produce only electric fields Power in AC Circuits I Charges in uniform motion (constant velocity) produce electric and magnetic fields An AC Circuit Problem I Charges that are accelerated produce electromagnetic radiation Transformers Resonance Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Electromagnetic Waves Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Maxwell’s viewpoint was: Power in AC Circuits I a changing magnetic field produces an electric field An AC Circuit Problem I if that electric field also changes, it produces a magnetic field Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Electromagnetic Waves are Transverse Waves Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I The electric and magnetic fields are perpendicular to the line of motion. Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Electromagnetic Waves are Transverse Waves Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I I The electric and magnetic fields are perpendicular to the line of motion. When you rotate E into B, you get the direction of motion. Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Electromagnetic Waves are Transverse Waves Class 14 Physics 106 Learning Outcomes I At a point where the electric field is large, the magnetic field is also large. Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Electromagnetic Waves are Transverse Waves Class 14 Physics 106 Learning Outcomes I At a point where the electric field is large, the magnetic field is also large. Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers I In a wave Emax = cBmax Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance The Electromagnetic Spectrum Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light The Spectrum of EM Waves Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit I Forms of electromagnetic waves exist that are distinguished by their frequencies and wavelengths Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light The Spectrum of EM Waves Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit I I Impedance Forms of electromagnetic waves exist that are distinguished by their frequencies and wavelengths Power in AC Circuits c = f λ = 3.00 × 108 m/s An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light The Spectrum of EM Waves Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Forms of electromagnetic waves exist that are distinguished by their frequencies and wavelengths Power in AC Circuits I c = f λ = 3.00 × 108 m/s An AC Circuit Problem I Wavelengths for visible light range from 400 nm to 700 nm Resonance I Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light The Spectrum of EM Waves Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Forms of electromagnetic waves exist that are distinguished by their frequencies and wavelengths Power in AC Circuits I c = f λ = 3.00 × 108 m/s An AC Circuit Problem I Wavelengths for visible light range from 400 nm to 700 nm Resonance I I There is no sharp division between one kind of em wave and the next kind Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light The EM Spectrum Class 14 Physics 106 Learning Outcomes I Note the overlap between types of waves Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light The EM Spectrum Class 14 Physics 106 Learning Outcomes I I Note the overlap between types of waves Visible light is a small portion of the spectrum Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light The EM Spectrum Class 14 Physics 106 Learning Outcomes I I I Note the overlap between types of waves Visible light is a small portion of the spectrum Types are distinguished by frequency or wavelength Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light How Is Light Created? Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light How Is Light Created? Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I Hot objects produce light I Some materials absorb ultraviolet energy and glow I Electrical energy can cause gases to glow I Chemical energy can cause gases to glow Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light How Is Light Created? Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance I Hot objects produce light I Some materials absorb ultraviolet energy and glow I Electrical energy can cause gases to glow I Chemical energy can cause gases to glow I Usually energy excites elecgrons in atoms. Atoms give off light as they return to their graound state. Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light What Are Some Characteristics of Light? Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light What Are Some Characteristics of Light? Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit I Reflection, refraction I Travels in straight lines I Formation of images I Transfers heat energy I Has wavelength, frequency Transformers I Can knock electrons out of atoms Maxwell’s Ideas I Experiences interference, diffraction (bending around corners) Impedance Power in AC Circuits An AC Circuit Problem Resonance Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light What Are Some Common Places Where We See Optics? Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light What Are Some Common Places Where We See Optics? Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits I Lenses, Mirrors An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light What Are Some Common Places Where We See Optics? Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits I Lenses, Mirrors I Surfaces of glass, water An AC Circuit Problem Resonance Transformers Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light What Are Some Common Places Where We See Optics? Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits I Lenses, Mirrors I Surfaces of glass, water Resonance I Droplets of water, bottles Transformers An AC Circuit Problem Maxwell’s Ideas Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light What Are Some Common Places Where We See Optics? Class 14 Physics 106 Learning Outcomes Phasors and the Series RLC Circuit Impedance Power in AC Circuits I Lenses, Mirrors I Surfaces of glass, water Resonance I Droplets of water, bottles Transformers I Metallic surfaces - spoons Maxwell’s Ideas An AC Circuit Problem Hertz and LC Circuits Electromagnetic Radiation Properties of Electromagnetic Radiation The Electromagnetic Spectrum Light
