Judge the equivalent resistance when the following are connected in parallel: $1 \, \Omega$,$10^3 \, \Omega$,and $10^6 \, \Omega$.

(D) When $1 \, \Omega$,$10^3 \, \Omega$,and $10^6 \, \Omega$ are connected in parallel,the equivalent resistance $R$ is given by the formula:
$\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$
Substituting the values:
$\frac{1}{R} = \frac{1}{1} + \frac{1}{10^3} + \frac{1}{10^6} = 1 + 0.001 + 0.000001 = 1.001001 \, \Omega^{-1}$
Therefore,$R = \frac{1}{1.001001} \approx 0.999 \, \Omega$.
In a parallel combination,the equivalent resistance is always less than the smallest individual resistance. Since $1 \, \Omega$ is the smallest,the result $0.999 \, \Omega$ is consistent with this principle.