In the given circuit, bulb A is $12\mathrm{.}0$ W and bulb B and C are each $9\mathrm{.}00$ W$.$ If the switch is open, what is the value of the current through bulb B$?($Assume the electrical outlet is an ideal DC battery with the potential difference equal to $120$V$.)$

Group of answer choices

$7\mathrm{.}50102$A

$4\mathrm{.}29102$A

$9\mathrm{.}45102$A