Question

A man has five resistors each of value $\frac{1}{5}\Omega$. What is the minimum resistance he can obtain by connecting them ?

• A. $\frac{1}{10}\Omega$
• B. $\frac{1}{5}\Omega$
• C. $\frac{1}{50}\Omega$
• D. $\frac{1}{25}\Omega$

Answer 1

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

Minimum resistance is obtained when all the resistance are connected in parallel.

Effective resistance in parallel connection $1\frac{1}{R_{min}}=\frac{1}{R}+\frac{1}{R}+....$ 5 terms

$⟹$ Minium resistance $R_{min}=\frac{R}{5}=\frac{1/5}{5}=\frac{1}{25}\Omega$