Question

Question 5 (b)
What is the lowest total resistance that can be secured by combinations of four coils of resistance $4\Omega ,8\Omega ,12\Omega$ and $24\Omega$?

Answer 1

(b) If these coils are connected in parallel, then the equivalent resistance will be the lowest.
When the resistances are connected in parallel ,the equivalent resistance is given by,
$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+\frac{1}{R_4}$
$=\frac{1}{4}+\frac{1}{8}+\frac{1}{12}+\frac{1}{24}=\frac{6+3+2+1}{24}=\frac{12}{24}=\frac{1}{2}$
$R=2\Omega$
Therefore, $2\Omega$ is the lowest total resistance.