Big and Small Resistors

The questions below are due on Monday September 15, 2025; 10:00:00 PM.
 
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For all parts of this problem, imagine you have the following three resistors:

  • r1 = 12\Omega
  • r2 = 20\Omega, and
  • r3 = 30\Omega.

Answer the following questions about resistances that can be made using all three resistors in some way.

What is the smallest resistance you can make by combining all three of these resistors together? Enter your answer as a single number, representing this resistance in Ohms.

What is the largest resistance you can make by combining all three of these resistors together? Enter your answer as a single number, representing this resistance in Ohms.

Is it possible to combine all three of these resistors somehow to create an equivalent resistance of 24\Omega? If so, enter a small expression below for how to create this value. Your expression should involve variables r1, r2, and r3, and you should use par(x, y) to represent a parallel combination of x and y, and ser(x, y) or x+y to represent a series combination of x and y. If it is not possible, enter IMPOSSIBLE instead.