Question

What is the smallest resistance you can make by combining them?

Answer 1

Answer:

166.67 ohm

Explanation:

Complete statement of the question is :

You have a collection of six 1.0 kO resistors. What is the smallest resistance you can make by combining them?

When we connect resistors in parallel, the combination resistance is always smaller than the smallest resistance value we combine.

Parallel Combination of resistances is given as

$\frac{1}{R_{p}} = \frac{1}{R_{1}} +\frac{1}{R_{2}} +\frac{1}{R_{3}} + ....$

where

$R_{p}$ = Equivalent resistance

and $R_{1} , R_{2}, R_{3}$ are resistances in parallel.

So for the above question, we have

$R_{1} = R_{2} = R_{3} = R_{4} = R_{5} = R_{6} = 1 kohm = 1000 ohm$

So parallel combination is given as

$\frac{1}{R_{p}} = \frac{1}{R_{1}} +\frac{1}{R_{2}} +\frac{1}{R_{3}} +\frac{1}{R_{4}} +\frac{1}{R_{5}} +\frac{1}{R_{6}}\\\frac{1}{R_{p}} = \frac{1}{1000} +\frac{1}{1000} +\frac{1}{1000} +\frac{1}{1000} +\frac{1}{1000} +\frac{1}{1000}\\R_{p} = \frac{1000}{6} \\R_{p} = 166.67 ohm$

So the smallest resistance is 166.67 ohm