Why Does io'' Equal Zero in Parallel Resistor Circuits?

[kougou]

hi, please have a look of the following picture.http://www.cramster.com/solution/solution/1175199




Do you guys get 0 for io'', why is it 0?

 

[willem2]

Because the potential difference between the points to the left and the right of the i_3 arrow is 0, because there's a wire between them with 0 resistance.

I = V * R and R is 0, so V = 0.

 

[DennisN]

Yes, I₀=0, because the path of i₃ is a short circuit. But Ohm's law is V=I*R (not I = V * R). This yields V=i₃*R, and since R=0, then V=0, regardless of i₃.

(V = potential difference between the points to the left and the right of i₃,
R = resistance between the points to the left and the right of i₃)

 

[DennisN]

A more formal explanation: Kirchhoff's voltage law (KVL) says "The directed sum of the electrical potential differences (voltage) around any closed circuit is zero." In the picture the path of i₃ and I₀ is a closed circuit. Since V=0, this means the voltage V_lower across the two lower resistors must be 0, which yields I₀ = V_lower/(R1+R2) = 0 V/6 kΩ = 0.

 

[ErolDynamics]

because there is a short circuit over there :D

 

[privateman]

Current always takes the shortest route, so therefore no current exists at R3, because resistance is proportional to the wire's length's .
electricity moves from a higher potential to a lower one.
Potential = current intensity x resistance, thus potential increases when resistance does.
eventually electricity will not choose the longer path because it has a higher potential.

Rab

 

[sophiecentaur]

Current always takes the shortest route, so therefore no current exists at R3, because resistance is proportional to the wire's length's .
electricity moves from a higher potential to a lower one.
Potential = current intensity x resistance, thus potential increases when resistance does.
eventually electricity will not choose the longer path because it has a higher potential.

Rab

OWCH that's Schoolboy Howler number one!
Current is SHARED between the possible paths it can take. If one path happens to be very low Resistance (IRRESPECTIVE OF LENGTH) then proportionally more current will take that path but SOME current will go through other paths.

The only time (in theoretical problems only) when 'all the current' flows along a particular path is when it has Zero Resistance (drawn as a line between two points on the schematic diagram) which is a Short Circuit. Real wires are never total short circuits.

 

[NewtonianAlch]

Sophiecentaur has nearly 5.5k posts here and is recognised as a science advisor, is it merited at all to have a go at someone here who's been helping people for a long time and has done a good job of it?

I don't know which resistor you're referring to as R3 here, but I'm inclined to agree with Sophiecentaur, if there's resistance, current is going to be shared between them no matter how low the resistance. In these kinds of problems, you're not meant to be worrying about wire lengths, that's not even stated in the problem, unless you want to unrealistically start assuming lengths.

Also:

so there's NO such thing as zero resistance as you say,
OWCH another howler back at ya

I believe this was already mentioned, read the post by SC again?

The only time the current is going down the "path of least resistance" is if there's a short somewhere, and even then that's only in theory as in the real-world there is resistance in a wire. That's my 2 cents.

 

[NewtonianAlch]

To the O.P.

Consider doing a quick re-draw of a circuit if it's not clear what's happening at first, this way you can see what's happening with the currents:

http://img560.imageshack.us/img560/1792/dsc0005ew.jpg

 

[DennisN]

I'm with Sophiecentaur and NewtonianAlch here. Sophie did a good thing by correcting a common misconception (that current always takes the shortest route is wrong), and also provided a short, excellent and correct description of how currents are divided between paths. No, in reality there are no connections with zero resistance (the closest thing would be superconductors, but today they're still a little difficult to implement for common use ).

I wish you all a good weekend!

 

[DennisN]

(Current paths update)
Image description: R₁ is a large resistance, R₂ is a small resistance (e.g. from a wire or inductor). We can see that a smaller resistance R₂ will result in a larger current I₂. I₁=V/R₁, so I₁ can in reality only get truly zero if the voltage V across R₁ is truly zero.
Note: R_total=R₁//R₂ means R₁ parallel with R₂; a smaller R₂ will result in a smaller R_total. (if anyone spots a typo, please say so, I'm a little tired at the moment )

And here's a link for Resistors in Parallel (see Example No3 in particular):
http://www.electronics-tutorials.ws/resistor/res_4.html