Thermistor Design Problem

The questions below are due on Tuesday April 02, 2019; 11:00:00 PM.

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In Design Lab 7, you worked with a device that produced a variable current based on the intensity of light. You then built a circuit to convert that variable current into a voltage signal could be used to determine the position of the light.

Devices which take energy (or information/signals) and convert them from one form into another (as in light intensity to voltage) are called transducers. In this question, we will look at designing a temperature-to-voltage transducer.

In order to do so, we will consider a temperature-variable resistor (a "thermistor"), whose resistance varies with the temperature of the device:

Throughout this problem, we will consider a thermistor whose resistance R_T is given by the following equation:

R_T = 10000e^{3977(\frac{1}{T}-\frac{1}{298})}

where R_T is the resistance of the thermistor in Ohms, and T is the temperature of the thermistor in Kelvin (remember Kelvin is measured with respect to "absolute zero," which is -273 degrees Celsius).

Calculating R_T

Define a Python function r_t(kelvin), which takes a temperature (in Kelvin) and returns the resistance of R_T, in Ohms, assuming that the thermistor is at whatever temperature is fed into the function.

You may find some functions from the math module helpful.

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Transduction Juction

For the remainder of the problem, we will consider the following temperature transducer circuit involving a Voltage Source of 10V, a fixed resistor R_b, and a thermistor with the characteristics described above.

A Sense of Direction

As the temperature goes up (for a fixed, finite, non-zero value of R_b), does the voltage V_{temp} go up, go down, or stay the same?

As the temperature goes up, V_{temp}

Choice

Now, say we wanted to design a thermometer of the form above, but for a particular application. Your design goal is to figure out a value for R_b to satisfy the following requirement: we want to be able to measure between 10 and 70 degrees Celsius (283 and 343 Kelvin), and the nature of our downstream circuit requires the difference between V_{temp} measured at these two temperatures (10 and 70) to be between 3.2V and 3.4V.

Determine an appropriate value of R_b, and enter it below.

There are several ways to solve this problem and a range of correct answers, but an easy way is to take advantage of the Python implementations you've already built and with a little guidance on your part, let Python find the answer for you rather than solve explicitly!.

Value of R_b in Ohms:

Thermometer

From the circuit above, we might be interested in measuring V_{temp} to determine the temperature. Write a Python function named temperature that takes as input a resistance Rb and a voltage Vt (representing the resistance R_b and the voltage V_{temp} in the circuit above, respectively), and returns a number representing the temperature in Kelvin at which that measurement was taken.

You may find some functions from the math module helpful.

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