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A cylinderical wire has a resistance of 21.0 ohm. It ismelted down, and from the same volume of metal a new cylindricalwire is made that is three time

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asked 2020-11-01
A cylinderical wire has a resistance of 21.0 ohm. It ismelted down, and from the same volume of metal a new cylindricalwire is made that is three times longer than the originalwire. What is the resistance of the new wire? I know that the answer is Rnew = 60 ohms, I just don't whatsteps to partake in to reach this solution, any help would be muchappreciated!

Answers (1)

2020-11-02
Resistance = ? L / A where A is the crosssection area and L is the length.
Notice that resistance of the wire is proportional to length(the longer, the higher resistance) and inv prop to area (thethinner it gets, the greater the resistance).
The key to this problem is recognizing that the volume of thewire stays the same (same amount of material) and the volumeis V = A L
So... if the length increases by a factor of 3, the area alsodecreases by a factor of 3!
What does this do to the resistance of thewire? Increasing its length increases resistance by afactor of 3 and decreasing area increases its resistance by afactor of 3. In all, the resistance increases by a factor of9.
I can't tell where you got the 60 ohms from, but for thiswire... if it started at 21 ohms and you then tripled its length,the resistance increases by a factor of 9 to 189ohms.
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