Call me delusional, but I can't shake the weird hunch that there's supposed to be a drawing to go along with this question, showing the values of the resistors and exactly how they're connected to the battery.
In a series circuit, the voltage divides across the resistors in proportion to their resistances. If two resistors in series are the only things connected to your battery, then the voltage across each resistor is . . .
(12 volts) x (the resistance of that one resistor) / (the sum of both resistors) .
Given there are three blocks of masses , and (ref image in attachment)
When all three masses move together at an acceleration a, the force F is given by
F = ( + + ) *a ................(equation 1)
Also it is given that does not move with respect to , which gives tension T is exerted on pulley by only, Hence tension T is
T = *a ..........(equation 2)
There is also also tension exerted by . There are two components here: horizontal due to acceleration a and vertical component due to gravity g. Thus tension is given by
T = ................(equation 3)
From equation 2 and 3, we get
*a =
Squaring both sides we get
* = * (+)
* = ( * )+ ( *)
( - ) * = *
= */( - )
Taking square root on both sides, we get acceleration a
a = *g/()
Hence substituting the value of a in equation 1, we get