Ordering Wires by Resistance: R, R/2, R/2 & 2L, R & 2L

[JSGandora]

If we have a set of cylindrical wires, which we know the radii and the lengths, how do we order them from least resistant to most resistant (assuming they are all the same material)?

An example:

Radii lengths are expressed in terms of $R$ and lengths of wires are expressed in terms of $L$.

R and L
R/2 and L
R/2 and 2L
R and 2L

 

[berkeman]

If we have a set of cylindrical wires, which we know the radii and the lengths, how do we order them from least resistant to most resistant (assuming they are all the same material)?

An example:

Radii lengths are expressed in terms of $R$ and lengths of wires are expressed in terms of $L$.

R and L
R/2 and L
R/2 and 2L
R and 2L

Welcome to the PF.

What is the equation that relates the resistance to the resistivity, cross-sectional area and length? That should make it clear.

 

[24hourtutor]

Even without knowing the equation, you should be able to find wire with the greatest resistance and the wire with the least resistance.

Just think: Is it harder (greater resistance) for an electron to travel a long distance down a narrow path or a short distance down a wide path?

Once you have those two, you'll have to think about whether the length or the radius affects the resistance more.

Andy
__________________________________________________________________________
In Boston? Need physics help? Send me an email!
the24hourtutor@gmail.com

 

[Subductionzon]

You should also know that ideally current flows on the outside surface of a wire. If the writer of the question assumed that it travels through the whole cross section of the wire he might arrive at a different answer than I would.

 

[Evil Bunny]

skin effect is frequency dependent, isn't it? I think DC current flows through the entire cross section... If you're talking 60 hertz like in your house, I think skin effect is pretty insignificant.

 

[JSGandora]

Thanks for all the responses.

So would this be correct?

It would be the easiest for current to move through a short and wide path and hardest for current to move through a long but narrow path, thus making the wire with dimensions R/2 and L to have the least current. Also, the wire with dimensions R and L/2 has the most current. Now it's only between R/2 & L/2 and R & L.

I think the radius affects the resistivity more than the length, therefore we have the current through the wire with dimensions R and L to be more than the wire with dimensions R/2 and L/2. Therefore we can order the current from least to greatest like this:

R/2 and L
R/2 and L/2
R and L
R and L/2

Is this correct?

 

[Subductionzon]

You are right Evil Bunny, I guess I am to used to dealing with AC. A quick Google search confirmed that skin effect is limited to AC,

So that is another question. Was it AC or DC in the problem?

 

[JSGandora]

The problem to which I am referring to does not specify. Here is the exact wording of the problem:

"Rank the following cylindrical conductors in descending order according to the current through them when the same potential difference V is placed across their lengths."

Then it shows a picture of all the cylinders with the specified dimensions.

 

[Subductionzon]

Thanks for all the responses.

So would this be correct?

It would be the easiest for current to move through a short and wide path and hardest for current to move through a long but narrow path, thus making the wire with dimensions R/2 and L to have the least current. Also, the wire with dimensions R and L/2 has the most current. Now it's only between R/2 & L/2 and R & L.

I think the radius affects the resistivity more than the length, therefore we have the current through the wire with dimensions R and L to be more than the wire with dimensions R/2 and L/2. Therefore we can order the current from least to greatest like this:

R/2 and L
R/2 and L/2
R and L
R and L/2

Is this correct?

You changed your question. Your original question was for least to most resistant, now you have it from least to greatest current. I like your order assuming DC, but make sure that your answer matches your question.

 

[Subductionzon]

The problem to which I am referring to does not specify. Here is the exact wording of the problem:

"Rank the following cylindrical conductors in descending order according to the current through them when the same potential difference V is placed across their lengths."

Then it shows a picture of all the cylinders with the specified dimensions.

Ah, worded that way it implies DC. AC would have a varying voltage and the proper term for AC voltage is RMS voltage, short for root mean square.

 

[JSGandora]

You changed your question. Your original question was for least to most resistant, now you have it from least to greatest current. I like your order assuming DC, but make sure that your answer matches your question.

Oh, my bad. Then by ordering resistance would just be the opposite right?

 

[Subductionzon]

Oh, my bad. Then by ordering resistance would just be the opposite right?

Yup. That was just a friendly warning. I wouldn't want you to get marked wrong when you understand how to do the problem correctly.

 

[JSGandora]

Oh, I see. Thanks a lot for your help!