Resistence and double stranded wire.

[zebra1707]

Homework Statement

I have been stuck with a problem regarding the resistance of a wire that is 2.0 meters long, has a resistance of 0.20 ohm. The wire has been cut in half and then the two ends of the new wires joined together to make a double standed wire.

We don't know what the diameter of the wire is - which I find a bit strange. I have worked our what the resistance of the two halves would be (0.10 ohm) - that is okay. Its the new double strand that has got me stumped.

Homework Equations

The Attempt at a Solution

Cheers Petra d.

 

[LowlyPion]

Homework Statement

I have been stuck with a problem regarding the resistance of a wire that is 2.0 meters long, has a resistance of 0.20 ohm. The wire has been cut in half and then the two ends of the new wires joined together to make a double standed wire.

We don't know what the diameter of the wire is - which I find a bit strange. I have worked our what the resistance of the two halves would be (0.10 ohm) - that is okay. Its the new double strand that has got me stumped.

Welcome to PF.

If you know the resistance of 1 strand, then maybe two strands could be figured as parallel resistors?

 

[zebra1707]

Thankyou for the welcome

Its the resistance of the "new" double stranded wire that has got me stumped.

Many thanks for taking the time to reply.

Cheers Petra d.

 

[LowlyPion]

Thankyou for the welcome

Its the resistance of the "new" double stranded wire that has got me stumped.

Many thanks for taking the time to reply.

Cheers Petra d.

Whether you consider that they are || resistors, or simply that you have doubled the cross sectional area of both resistors - halving the equivalent resistance - I think you get the same result.

 

[zebra1707]

Hi there

Thank you for the reply. Not sure that I understand your response.

I think what you are saying is that the resistance of the wire will not change - even though it is now double-stranded??

Full strand of wire is 2.0 meters = 0.2 ohm resistance
1/2 stand is 1.0 meters = 0.1 ohm (I understand this relationship)

1/2 stands have now become double-strand (still 1.0 meter in length) - what is the resistance and the relationship. Note that I do not have a diameter of the wire.

Cheers Petra

Whether you consider that they are || resistors, or simply that you have doubled the cross sectional area of both resistors - halving the equivalent resistance - I think you get the same result.

 

[LowlyPion]

No. You don't understand.
Yes you chopped the wire in half.
Yes the length is now half and each resistor's resistance is half.

But you twisted them together - essentially made them parallel.
The equivalent resistance of that would be given by calculating the resistance for 2 parallel resistors.

1/R_eq = 1/R + 1/R = 1/.1 + 1/.1 = 20

R_eq = 1/20 = .05

Looking at it another way, a resistor's resistance is proportional to length. The longer it is the greater the resistance. It is inversely proportional to cross sectional area.The greater the area, the less the resistance. While it's true you don't know the diameter, you do know that since you have now 2 cross sections of the same thing it is twice as much area - whatever it is.

So while R = ρ*L/A if you take 1/2 the original L and double the A you get

R_eq = ρ*(L/2)/(2A) = 1/4*ρ*L/A = 1/4*R = 1/4*.2 = .05

http://en.wikipedia.org/wiki/Electrical_resistance#DC_resistance

 

[zebra1707]

HI there

Many thanks - this has clarified it for me.

Cheers Petra d.