Question

A student has 10 resistors, each of resistance r. The minimum resistance that can be obtained by him using these resistors is

(a) 10r

(b) \(\frac{r}{10}\)

(c)\(\frac{r}{100}\)

(d) \(\frac{r}{5}\)

Answer 1

Correct answer is (b) \(\frac{r}{10}\)

Answer 2

This question is not too difficult to answer. If you combine all the resistors in parallel then you will get the minimum resistance value. If you combine in series definitely you will get the large vaule. 

In order to find the minimum value of resistance then- 

\(\frac{1}{R_eq}=\frac{1}{R_1}+\frac{1}{R_2}+...+\frac{1}{R_n}\)

Put the value of resistance r in above equation, we get- 

\(\frac{1}{R_eq}=\frac{1}{r}\times 10=\frac{10}{r}\)

Then, \(R_eq =\frac{r}{10}\)