Validity of Kirrchoff's Laws in Electrical Circuits

[ehabmozart]

Homework Statement

a) Find the current through the battery and each resistor inthe circuit shown.
b) What is the equivalent resistance of the resistornetwork?

http://s3.amazonaws.com/answer-board-image/db89d3f298e4098e8852b10c30cb3f53.jpg

Homework Equations

Kirrchoff's laws

The Attempt at a Solution

I have one BIG doubt. The answer says that (whatever the number is), there is a current through R1. We were told in class that a current would prefer a clean path. Since there is a nice wire at the top, shouldn't this avoid any current to pass through R1? ... Thanks for helping

 

[Doc Al]

I have one BIG doubt. The answer says that (whatever the number is), there is a current through R1. We were told in class that a current would prefer a clean path. Since there is a nice wire at the top, shouldn't this avoid any current to pass through R1? ... Thanks for helping

No. That "nice wire" at the top just connects to R2. If there were two points where R1 and just a wire were in parallel, then you'd be correct.