Simple Lazy Current Question (Circuit)

[seto6]

ok this is what i have, i want to know if the current would go through the 12V and 4k ohm resistor, since there is a short path (by making the inductor a short for time = infinity) would the current be lazy and take the path through the short or would it also go through the 12v and 4k ohm.

 

[berkeman]

ok this is what i have, i want to know if the current would go through the 12V and 4k ohm resistor, since there is a short path (by making the inductor a short for time = infinity) would the current be lazy and take the path through the short or would it also go through the 12v and 4k ohm.

What are your thoughts? What is the resistance in Ohms for a short circuit? What is the voltage divider equation?

 

[CEL]

You must remember that the current through the short circuit comes from the two voltage sources.