DQ12B_solution

DQ12B_solution - Discussion Question 12B P212 Week 12...

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Discussion Question 12B P212, Week 12 Phasors Next, we encounter the rich subject of driven RLC circuits . The most basic example is shown in the diagram: a resistor, a capacitor, and inductor, and an AC generator all connected in series. The generator is just a fancy type of battery that produces not a constant “DC” voltage as we have encountered so far, but an oscillating “ AC ” voltage. The voltage from the generator oscillates sinusoidally at some angular frequency ω , and has a maximum magnitude E max (also called the “amplitude” or “ peak voltage ”). If the AC generator weren’t present, our circuit would be a plain old undriven LC circuit with some resistance R thrown in. It would support a nice oscillating current of frequency ω 0 = 1/ LC … except the resistor would damp out the oscillations over time. To keep the circuit going, we attach the generator to drive the oscillations. But … the AC generator is driving the circuit at its own frequency ω , which need not be the same as the circuit’s resonant frequency ω 0 . The result is something of a mess. / The generator forces the current to oscillate at frequency ω , but if ω doesn’t match ω 0 , the driving voltage will be out of phase with the current. To help us visualize what is going on, we use phasors . A phasor is just a way of graphically representing the time-dependence of something which oscillates . Specifically, a phasor is a vector in the xy plane. We then imagine that this vector rotates around the origin in a counterclockwise direction, with angular velocity ω radians/second. The phasor describes the behavior of something oscillating with frequency ω

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DQ12B_solution - Discussion Question 12B P212 Week 12...

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