p240_ct23_f07 - Physics 240 Fall 2007 Lecture #23 Review...

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Physics 240 Fall 2007 Lecture #23 Dr. Dave Winn 2405 Randall Lab winn@umich.edu Review Sessions: Tue and Wed 8-10pm 182 Dennison
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Driving electrical oscillators with AC Electrical oscillators can be driven with AC generators All such “forced oscillations” take place at the driving frequency ω d Details of the oscillation depend on response of oscillator! Driving EMF: ξ = ξ max sin( ω d t)
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Understanding driven AC circuits There are only a few basic principles, we will try to focus on these Though AC circuits are less intuitive, they offer one huge practical advantage, the ability to exchange Voltage and Current To understand how to analyze AC circuits, focus on how each circuit element behaves when “driven” by an AC generator In the following voltage plots we will graph V i -V f for each device as we go “through” it with the current.
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How does a resistor respond to AC? From Ohm’s law, we have just V=IR, so: I(t) = ξ / R I(t) = ξ 0 sin( ω d t) / R These two things, current and voltage across the resistor, change together; they are said to be “in phase” with one another
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How does a capacitor respond to AC? Current must flow for a while before the capacitor can be charged! This means current must come before voltage In an AC circuit with a capacitor the current leads the voltage by 90 °
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How do inductors respond to AC? Current must change to have voltage across an inductor! Maximum voltage when current changes most rapidly; voltage must rise before current. In and AC circuit with an inductor current lags voltage by 90 °
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An AC generator drives a single circuit element. Given these plots describing the voltage and current as a function of time, what kind of circuit element is this? 1. Resistor 2. Capacitor 3. Inductor Current leads voltage
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An AC generator drives a single circuit element. Given these plots describing the voltage and current as a function of time, what kind of circuit element is this? 1. Resistor 2. Capacitor 3. Inductor Current in phase with voltage
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Phasors, Currents, and Voltages Allow I 0 and V 0 to be complex numbers (phasors). Multiply by e j ω t and take the real part to get current or voltage as a function of time. Eulers Formula e j ω t =cos( ω t)+j*sin( ω t) Taking the “real” part is equivalent to projecting onto the horizontal axis http://www.falstad.com/euler/ A phasor is a complex constant (a vector in the complex plane)
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Impedance Impedance (Z) is generalized resistance for an AC circuit.
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p240_ct23_f07 - Physics 240 Fall 2007 Lecture #23 Review...

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