Question

How should the two resistances of 8 $\Omega$ each must be connected to produce an equivalent resistance of 4 $\Omega$ ?

Answer 1

As the resultant resistance is lesser than the individual resistances.
The arrangement of the system should be in parallel.
We can prove it with the help of this formula,

$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}\frac{1}{R}=\frac{1}{8}+\frac{1}{8}\frac{1}{R}=\frac{1+1}{8}\frac{1}{R}=\frac{2}{8}\frac{1}{R}=\frac{1}{4}\therefore R=4\Omega$