Question

A connection is made consisting of resistance A in series with a parallel combination of resistances B and C. Three resistors of value 10 $\Omega$, 5 $\Omega$, 2 $\Omega$ are provided. Consider all possible permutations of the given resistors into the positions A, B, C and identify the configurations with maximum possible overall resisatance, and also the ones with minimum possible overall resistance. The ratio of maximum to minimum values of the resistances (up to second decimal place) is

• A. 2.143

Answer 1

The correct option is A 2.143

The connection of resistors is as shown below:
Given resistor values are : 10 $\Omega$, 5 $\Omega$, 2 $\Omega$
The maximum resistance possible is,
$R_{T(max)}=10\Omega +\left(5\Omega ||2\Omega \right)$

$=(10+\frac{10}{7})\Omega =\frac{80}{7}\Omega$
The minimum resistance possible is,

$R_{T(min)}=2\Omega +\left(10\Omega ||5\Omega \right)$

$=(2+\frac{10}{3})\Omega =\frac{16}{3}\Omega$

$\frac{R_{T(max)}}{R_{T(min)}}=\frac{80/7}{16/3}=\frac{15}{7}=2.143$