Suppose you have a supply of inductors ranging from \(1.00{\rm{ }}nH\) to\(10.0{\rm{ }}H\), and resistors ranging from \(0.100{\rm{ }}\Omega \) to\(1.00{\rm{ }}M\Omega \). What is the range of characteristic \(RL\) time constants you can produce by connecting a single resistor to a single inductor?

A resistor is a passive electrical device with two terminals that creates electrical

resistance to serve as a circuit element.

Reducing current flow, regulating signal levels, dividing voltages,

biassing active devices, and terminating transmission lines are just a few

of the many uses for resistors in electronic circuits.

• The inductance range is:\(1.00{\rm{ }}nH - 10.0{\rm{ }}H\)
• The resistance range is: \(0.100{\rm{ }}\Omega - 1.00{\rm{ }}M\Omega \)

Thelowesttimeconstantwillbeobtainedbyobtainingthelowestinductanceand

the maximum resistance values. This will provide us with

\({\tau _{\min }} = \frac{{{L_{\min }}}}{{{R_{\max }}}}\)

We will numerically have

\(\begin{array}{c}{\tau _{\min }} = \frac{{{{10}^{ - 9}}}}{{{{10}^6}}}\\ = \underline {1ps} \end{array}\)

The largest time constant will be obtained by obtaining the highest inductance and

the lowest resistance values. This will provide us with

\({\tau _{\max }} = \frac{{{L_{\max }}}}{{{R_{\min }}}}\)

We will numerically have

\(\begin{array}{c}{\tau _{\max }} = \frac{{10}}{{0.1}}\\ = \underline {100\;s} \end{array}\)

Combining, the range we can cover is

\(1ps < \tau < 100\;s\)

Therefore, the range is from \(1ps\) to \(100\;s\).