Electric Circuits - Mission EC8 Detailed Help

In the circuit below, if ammeter Azreads 6 A, then ammeter Axwould read ____ amps and ammeter Aywould read ____ amps.

(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

Current in Parallel Circuits:
Parallel circuits are characterized by branching locations. At each branching location, the current is divided into separate pathways. The overall current approaching the branch is equal to the sum of the current values in each individual branch. This can be expressed in equation form as:
Itot= I1+ I2+ I3+ ...
where Itot is the current outside the branches (and through the battery) and I1I2 and I3 are the current values in the individual resistors.

This question asks you to make comparisons of the current within two different branches of a parallel circuit (locations X and Y) to the current outside the branches (location Z). The current at location Z will be equal to the sum of the currents in the individual branches. The current within the branches themselves is inversely related to the resistance of the branches. Thus, the branch with less resistance will have a greater current. In fact, if branch Y has one-half the resistance if branch X, then its current will be two times the value of branch X. So you are looking for an answer that meets the following two criteria:
  • The sum of the current in branches X and Y equals the current at location Z.
  • The current in the branch with one-half the resistance will be two times the current in the other branch.