Question

What is the minimum resistance which can be made using five resistors each of $\frac{1}{5}\Omega$?

• A. $\frac{1}{5}\Omega$
• B. $\frac{1}{25}\Omega$
• C. $\frac{1}{10}\Omega$
• D. $25\Omega$

Answer 1

The correct option is B $\frac{1}{25}\Omega$

Minimum resistance will be achieved when all the resistors are connected in parallel.
$\frac{1}{R_{min}}=\frac{1}{\left(\frac{1}{5}\right)}+\frac{1}{\left(\frac{1}{5}\right)}+\frac{1}{\left(\frac{1}{5}\right)}$ $+\frac{1}{\left(\frac{1}{5}\right)}+\frac{1}{\left(\frac{1}{5}\right)}$

$\Rightarrow$ $\frac{1}{R_{min}}=5+5+5+5+5=25$

$\Rightarrow$ $R_{min}=\frac{1}{25}\Omega$