Solve for Equivalent Resistance - Resistor is shorted?

[zr95]

Homework Statement

I'm studying for a test and since this is technically a textbook problem I figured I'd post here to prevent being flagged.

I have the circuit redrawn.

Homework Equations

Series: Req = R1+R2...
Parallel: 1/Req= 1/R1 + 1/R2...

The Attempt at a Solution

I want to understand why when solving this circuit for Req it is (3 || 30) || 7.5 = 2ohms.
According to the solution I'm looking at the 75 ohm resistor is considered a short and no current flows across this? I don't understand why this is the case.

Also I was originally trying to be lazy and solve and just add things up without redrawing the circuit and ended up with 2ohms by doing:
((5||20)+2)||3 = 2ohms
Was this just coincidence?

 

[Fightfish]

I want to understand why when solving this circuit for Req it is (3 || 30) || 7.5 = 2ohms.
According to the solution I'm looking at the 75 ohm resistor is considered a short and no current flows across this? I don't understand why this is the case.

That is because the 75 ohm "resistor" is connected in parallel with a zero resistance piece of wire.

Also I was originally trying to be lazy and solve and just add things up without redrawing the circuit and ended up with 2ohms by doing:
((5||20)+2)||3 = 2ohms
Was this just coincidence?

Nope, its not a coincidence - if you deform the circuit, your consideration is correct.

 

[zr95]

You da man. That makes a lot of sense.