Seeing the Light
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In this problem, we will consider circuits that are designed to power two different light bulbs simultaneously. We will assume that our light bulbs can be modeled as 5\Omega resistors, and that the brightness of each is proportional to the power dissipated by it. As a proxy, in this problem we'll concern ourselves with the voltage drop across each resistor.
For example, if the bulbs are hooked up as follows, the voltage drop across each bulb will always be 5V, and so their brightnesses will always be equal:
Now, we wish to use a 10{\rm k}\Omega potentiometer to provide the bulbs with a variable voltage, much like we saw in lab.
Recall that a potentiometer is a three-terminal device that can be modeled as two separate resistors, whose values depend on \alpha (the normalized angle of the pot's mechanical shaft):
For each of the circuits on the following page, sketch a graph of the voltage drops across B_1 and B_2 versus \alpha (note that you do not have to solve for this relationship exactly). Label key values (endpoints, slopes, etc), including units.
For this question, assume that all op-amps are ideal and are powered with +10{\rm V} and 0V. Unlike in other problems so far, do NOT ignore output limitations of the op-amps.
Upload your answers as a single PDF file, including both your answer and your
work. Please do not include any identifying information in your submission
so that we can grade the submissions anonymously.
