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If a resistance of $0 \Omega$ and $x$ (and $x>0$) are in parallel does all current pass through the $0$ resistance?

For instance in the following circuit:

enter image description here

Set variable resistor to o ohms:

I know that current takes the path of least resistance but surely some would still go through the $12$ ohm resistor?

I am asking why no current goes through the higher resistance. If the lower resistance was 1 (from the variable resistor) the current would go through the higher resistor, so why when the lower resistance is 0 does all the current go through it.

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closed as off-topic by Bill N, ZeroTheHero, Jon Custer, Yashas, Kyle Kanos Mar 17 '17 at 9:38

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  • $\begingroup$ With $R_3=0 \;\Omega$, total resistance including $R_1$ would be $6+0 =6\;\Omega$ $\endgroup$ – Henry Mar 16 '17 at 14:53
  • $\begingroup$ Think of what voltage you'll see across the 2 parallel resistors, and from that work out the current through R2. $\endgroup$ – hdhondt Mar 21 '17 at 8:50
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$14 V, R=(6+0)\Omega=6\Omega$, thus $I=V/R= 14/6 A$. This current will flow through the battery and $R_1$ (and through the ZERO $\Omega$ resistor $R_3$).
No current will flow through $R_2$. The potential difference over $R_2 = 0$.

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