Electric Circuits - Mission EC8 Detailed Help

A 12-V battery, a 12-ohm resistor and a 6-ohm resistor are connected as shown below. The current in the 6-ohm resistor is ____ that in the 12-ohm resistor.
 
(Note: The numerical values above are selected at random and may differ from your values.)


 
Branch Currents in Parallel Circuits:
The current in an individual branch of a parallel circuit is dependent upon the voltage drop across the branch and the resistance of the resistor within the branch. The voltage drop across a branch in a parallel circuit is equal to the voltage rating of the battery. Thus, the current in a branch can be calculated as 

   Ibranch= ∆Vbattery/ Rbranch


  
This question asks you to make comparisons of the current in two separate branches within a parallel circuit. The current in a branch is directly related to the voltage drop across the branch and inversely related to the resistance of the branch. The voltage drop of each branch is the same. So the variable that will affect the current is the resistance value of each branch. Because of the inverse relationship, a greater resistance will result in a smaller branch current. In fact, four times the resistance will result in one-fourth the current.