$\tau_{max} = 100 \textrm{ s}$

$\tau_{min} = 1.00 \times 10^{-15} \textrm{ s}$

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This is College Physics Answers with Shaun Dychko. We have inductors ranging from a minimum of 1 nanohenry to a maximum of 10 henrys and some resistors ranging from 0.100 ohms upto 1 mega-ohms and we are asked to figure out what is the range of possible time constants we could make? So, the time constant is going to be the inductance divided by resistance. So to get the maximum time constant we want to maximize the numerator and minimize the denominator and so we will take maximum inductance divided by minimum resistance So that’s 10 henrys divided by 0.100 ohms which is 100 seconds will be the maximum time constant. And then for the minimum time constant, we want to minimize the numerator and maximize the denominator so we have 1 times 10 to the minus 9 henrys is the minimum inductance, that’s 1 nanohenry and we will divide that by 1 megaohm resistance which is 1 times 10 to the minus 15 seconds so that’s one femtosecond.