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Unformatted text preview: Lecture S10 Muddiest Points General Comments In today’s lecture, we began looking at circuits that include inductors. We saw that when using the node method, inductors fit into our scheme less easily than capacitors, although it can be done. We also did three concept tests on inductors, meant to demonstrate how inductors behave in simple circuits. The fundamental concept is that inductors resist current change (not currents!). The results of the concept tests follow from this principle. Responses to MuddiestPartoftheLecture Cards (45 cards) 1. What is the intensity of the light bulbs actual ly related to, current, voltage, or power? (2 students) For any given light bulb, the voltage and current are related — there is a curve of current vs. voltage that describes the constitutive law of the bulb. Of course, the power is just iv . So if you specify either i or v , you know the total power. The brightness is most directly related to the power, which can be determined from either i or v , through the constitutive law. 2. How do we know that s is frequency? (1) Very often, we take s = jω , where j = √ − 1. ω is the frequency in radians per second. For s = jω , st e = cos ωt + j sin ωt (14) (This is Euler’s formula.) I think it’s clear why ω is frequency — so s is a generalization of frequency. 3. If we know what the impedance of a capacitor is, why don’t we use them in the node method instead of the differential equations? (1) Today, I was trying to show how inductors enter the picture, and so backed up a little. In general, we can go directly to impedances, but we must always remember that we are solving differential equations — we can’t treat the impedances too literally as resistances....
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 Fall '05
 MarkDrela
 Differential Equations, Inductance, Inductor, RL circuit

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