Two solenoids, wound from wire from the same spool, have the same length and cross$-$sectional area, but solenoid #$1$ has half the turns of solenoid #$2.$ If these solenoids are each connected to a circuit, and the only non$-$negligible resistance is that of the solenoids, which solenoid gives the greater time constant and by what factor?

Group of answer choices

#$1$ by a factor of $2$

#$2$ by a factor of $2$

#$2$ by a factor of $4$

None of these choices.