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Rateofchange indicatorExperiment: Rateofchange indicatorPARTS AND MATERIALS
The potentiometer value is not especially critical, although lowerresistance units will, in theory, work better for this experiment than highresistance units. I've used a 10 kΩ potentiometer for this circuit with excellent results.
CROSSREFERENCES Lessons In Electric Circuits, Volume 1, chapter 13: "Capacitors"
LEARNING OBJECTIVES
SCHEMATIC DIAGRAM
ILLUSTRATION
INSTRUCTIONS Measure voltage between the potentiometer's wiper terminal and the "ground" point shown in the schematic diagram (the negative terminal of the lower 6volt battery). This is the input voltage for the circuit, and you can see how it smoothly varies between zero and 12 volts as the potentiometer control is turned fullrange. Since the potentiometer is used here as a voltage divider, this behavior should be unsurprising to you. Now, measure voltage across the 1 MΩ resistor while moving the potentiometer control. A digital voltmeter is highly recommended, and I advise setting it to a very sensitive (millivolt) range to obtain the strongest indications. What does the voltmeter indicate while the potentiometer is not being moved? Turn the potentiometer slowly clockwise and note the voltmeter's indication. Turn the potentiometer slowly counterclockwise and note the voltmeter's indication. What difference do you see between the two different directions of potentiometer control motion? Try moving the potentiometer in such a way that the voltmeter gives a steady, small indication. What kind of potentiometer motion provides the steadiest voltage across the 1 MΩ resistor? Calculus Differentiation, calculus Derivative, calculusIn calculus, a function representing the rate of change of one variable as compared to another is called the derivative. This simple circuit illustrates the concept of the derivative by producing an output voltage proportional to the input voltage's rate of change over time. Because this circuit performs the calculus function of differentiation with respect to time (outputting the timederivative of an incoming signal), it is called a differentiator circuit. Computer, analog Analog computerLike the averager circuit shown earlier in this chapter, the differentiator circuit is a kind of analog computer. Differentiation is a far more complex mathematical function than averaging, especially when implemented in a digital computer, so this circuit is an excellent demonstration of the elegance of analog circuitry in performing mathematical computations. More accurate differentiator circuits may be built by combining resistorcapacitor networks with electronic amplifier circuits. For more detail on computational circuitry, go to the "Analog Integrated Circuits" chapter in this Experiments volume.


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