Question

You have a collection of six 2.1 kΩ resistors. What is the smallest resistance you can make by combining them? Express your answer with the appropriate units. 

Answer 1

The smallest resistance can be obtained by connecting all these resistance in parallel.

Further,

For \(\mathrm{N}\) equal resistors in parallel, the reciprocal sum expression simplifies to:

\(\frac{1}{R_{\text {total }}}=\frac{1}{R} \times N\)

and therefore to:

\(R_{\text {total }}=\frac{R}{N}\)

So, Rsmallest \(=\left(2.1 \times 10^{\wedge} 3\right) / 6=350 \mathrm{Ohm}\)