A ductile metal wire has resistance R. What will be the resistance of this wire in terms of R if it is stretched to three times its original length, assuming that the density and resistivity of the material do not change when the wire is stretched? (Hint: The amount of metal does not change, so stretching out the wire will affect its cross-sectional area.)

Question

Accepted Answer

Hi everyone today, we are going to be determining the rods resistance in terms of our where a craftsman fabricates the rod to create a new one that has four times the length of the original one. But assuming that the new rod will have the same density receptivity and all material is going to be conserved. So in this particular example, we know for sure that L knew Is going to be four times l. And the way we want to tackle this problem is to by using this formula right here recall that resistance of cable or a cylindrical dimension is going to be given by R equals row, multiplied by L over A. Where in this case the row is the resistance city, the L. Is the length and the A is the cross sectional area of the rot. Are is going to be our assistance. So in this particular practice, we know that it is given the volume of the new rod is going to be the same as the old one, which is pretty much meaning that the craftsman is just stretching the whole rot. So we know that the volume is given by multiplying area. Cross sectional area with the link and we're told that the roads volume remains the same upon stretching. So, because of that, now we can find what the new uh area is using this conservation of volume. Okay, so the new volume is going to be the new cross sectional area, multiplied by the new length equals to the old cross sectional area, multiplied by the old cross the old length. So a new is the one that we want to find. And then L knew is four times L. And this is going to be A L. So we can cross out this L. Here and then we can find that a new is going to equals 1.4 A. Awesome. We know that the festivity is going to be the same because it is given here and the same dance steaming in the same volume here and therefore we can actually start solving this problem by creating a ratio or comparison between the new and the old are Okay so our new is going to be row multiplied by L. Knew what supplied by a new and then you can just substitute the army here and the menu here, Row multiplied by four. Um L Divided by 1/4 a. So our new Is going to be moving this forward, multiplied by this floor is going to be 16 row l over a. And recall that the row l over a. Here is going to be pretty much are old are just like, so oops, I will do a better job there there and then therefore we can conclude that our new is going to be equals to 16 are just like, so hey and that will corresponds to option a in this problem and that will be all for this particular problem. If you guys are still confused on this. There are other lesson videos regarding this particular topic. so please check it out. But that will be all for this particular example. Thank you.

Verified Solution

Key Concepts

Resistance

Effect of Length on Resistance

Cross-Sectional Area