You are given four resistors each having resistance of R ohm. Find the maximum and minimum resistance that can be made with these four resistors.

Given,

• Value of each resistor = R ohm

Maximum resistance

To get the maximum resistance, connect all four resistors in series combination where the total resistance $\text R_\text S$ of the combination is given by,

$\text R$\text S = \text R + \text R + \text R + \text R \\[1em] \Rightarrow \text R\text S = 4\text R

Minimum resistance

To get the minimum resistance, connect all four resistors in parallel combination where the total resistance $\text R_\text P$ of the combination is given by,

$\dfrac{1}{\text R_ \text P} = \dfrac{1}{\text R} + \dfrac{1}{\text R} + \dfrac{1}{\text R} + \dfrac{1}{\text R} \\[1em] \Rightarrow \dfrac{1}{\text R_ \text P} = \dfrac{4}{\text R} \\[1em] \Rightarrow \text R_\text P = \dfrac{\text R}{4}$

Hence, the maximum resistance is $\textbf {4R}$ and minimum resistance is $\dfrac{\textbf R}{\bold 4}$.