Three wires of resistance $1\Omega$, $2\Omega$, and $3\Omega$ respectively are connected in parallel. The equivalent resistance of the circuit is

For a parallel combination of resistors, the equivalent resistance $R_{eq}$ is found using the formula:
$$\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$$
Substitute $R_1=1$, $R_2=2$, and $R_3=3$:
$$\frac{1}{R_{eq}}=\frac{1}{1}+\frac{1}{2}+\frac{1}{3}$$
Find the common denominator, which is $6$:
$$\frac{1}{R_{eq}}=\frac{6+3+2}{6}=\frac{11}{6}$$
Taking the reciprocal gives:
$$R_{eq}=\frac{6}{11}\Omega$$