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Phasor diagrams for series RLC circuit (b) X L X C and (c) X L
Is this making sense? So bottom line. When you observe from any inertial frame (i.e. if you are "at rest") and watch particles move in circles, there must be a true, physical force which pushes those particles in towards the center of the circle (a centripetal force) to make them go in uniform circular motion. Gravity is the physical force for planets going in circles, the magnetic field creates the physical force for protons running in circles in a cyclotron...
Graph of current amplitude I vs source frequency w for a series RLC circuit with various values of circuit resistance. The resonance frequency is at w = 1000 rad / sec (where the current is at its maximum)
A full-wave diode rectifier circuit. (LAB)
The confusing thing is that CAPA said "uncharged" -but the thing is, when you connect those capacitors to that battery on the left, the capacitors can't stay uncharged for long! This is the ambiguous part of the capa problem - what we're doing in this circuit is a little dicey. You see - you're DIRECTLY connecting the top of one capacitor to the top of a battery with an ideal wire, and the bottom of the other capacitor to the bottom of the battery, again with an ideal (R=0) wire, there is no resistance in the connection of capacitor to battery! So the "RC" time constant for charging up the capacitor is actually zero! So *wham*, you dump charges really quickly onto the capacitor. Thus, even though CAPA said the capacitors are initially uncharged (which is correct, and tells you that Q1=Q2), they won't STAY uncharged for more than a split second.
So what the first two questions SHOULD have said is, "With a potential difference (V[battery]) across the combination, after waiting just long enough for the circuit to reach a nice steady state, what is the potential at point a (and, point b for the next question)." What CAPA didn't explicitly say was "after waiting just long enough for the curcuit to reach a nice steady state". CAPA didn't bother saying this because, as I just argued above, it takes 0 seconds for that to happen! But in real life, even wires have SOME real resistance. It will take a split second. But it sure won't take long, and then the answer to the question won't change any more or forever, as long as you don't mess with the switch - which is the third question!
Alternating Current Circuits and Electromagnetic Waves
Phasors and AC(sec. 31.1) Resistance and reactance(sec. 31.2) RLC series circuit(sec. 31.3) Power in AC circuits(sec. 31.4) Resonance in AC circuits (sec.
In 1800, Young did an experiment which very conclusively showed that light is a wave. (He observed that light interferes with itself, like waves do, whereas particles do NOT! I can tell you more about interference if you don't know about it) So by the time Maxwell came around, like 50-60 years later, the idea that light was a wave was VERY well established. But nobody knew what was "waving", that's really what Maxwell helped us figure out - it was the E and B fields! For the next 40 years, all was well - light is simply an electromagnetic wave, the math was simple, physicists got pretty cocky! Then things began to get a little confusing, and evidence started piling up that, in many circumstances, light also behaves like a particle after all! But it was strange, because in *some* respects it's unambiguously a wave, and in other respects it's unambiguously like a stream of particles.
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AC Circuits Physics 102 Professor Lee Carkner Lecture 24.
If I recall correctly, when learning about Uniform Circular Motion in Physics 1110, we learned that there was really no such thing as a "centripetal force." We said that such forces should actually be called "centrifugal forces."
AC Circuits Physics 102 Professor Lee Carkner Lecture 23.
"Centripetal" means "center-seeking". In an inertial reference frame (which is what we always use in Phys 1110 and 1120!) Newton's laws hold. Any object moving around a circle MUST feel a force that keeps it going in a circle (otherwise it will, of course, just go in a straight line, as Newton's first law would demand!) Now, what force would make an object go in a circle? You would have to have a force that pushes it towards the CENTER of the circle at all points. (Can you visualize that? Just take ONE step tangent to the circle, and ask "which way would a force be *needed* to make me move in a circular path?) That's centripetal. Think of the moon orbiting the earth. Why doesn't it just "run away"? Because the earth PULLS it, towards us. At all times in its orbit, the moon feels a steady pull towards planet earth, a centripetal force. Any object which goes in a circle needs such a centripetal pull.
AC Circuits PH 203 Professor Lee Carkner Lecture 23.
I'll do a simple demo in class at some point soon where I swing a (special, fairly robust) fluorescent bulb in a big circle. You'll be able to "see" the flickering then, because it will be on at certain positions on the circle, and off at others, so you'll see a sort of "dashed line" instead of a continuous streak.
l l portunity to organize the first circle of tors.
Important clarification on CAPA #9, problems 6-8
Hi Professor - I am working on CAPA set 9, and have some confusion about numbers 6-8. The problem is given with the capacitors uncharged, but then the questions seem like their answers would vary based on how long the circuit has ben in existence....how can the capacitors be uncharged when they are connected to a battery?
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