Math 212
Name: __________________________________
Homework 1
1. Though the resistance of an ideal resistor is constant, the resistance of a store-bought resistor
typically depends on both the temperature of the resistor and the amount of current flowing through it.
(a) A certain resistor is observed to have 150.23 ohms resistance when 3.0 amps of current are run
through it. After ten minutes, the temperature of the resistor has increased from 21 °C to 51 °C, and
the resistance has increased to 150.83 ohms, with the current unchanged. Based on this data, what
do you expect the resistance will be when the temperature of the resistor reaches 60 °C?
(b) Based on the data you have, find an approximate linear formula for the resistance V of the resistor as
a function of temperature X , assuming a current of 3.0 amps.
(c) The same resistor is cooled off and moved to a different circuit. In the new circuit the resistor carries
5.0 amps of current, and is observed to have a resistance of 150.49 ohms at a temperature of 27 °C.
Based on this data, find an approximate linear formula for the resistance V of the resistor as a
function of the temperature X and the current M .
2. The following figures show cross-sections of the function 0 aBß Cb for several values of C:
Cœ!
Cœ"
Cœ#
Cœ$
Using this information, make a rough contour plot of the function 0 aBß Cb. Include the contours for
the values ", #, $, %, and &:
PRACTICE SPACE
FINAL ANSWER