resistance of a wire.

Thread Starter

strantor

Joined Oct 3, 2010
6,782
I'm reading this book.
It has a little quiz at the end of each chapter. one of the questions is
"A wire is replaced with one that is twice as long and one half the diameter. It's resistance will be:
A. one-fourth
B. four times
C. eight times
D. the same"

My answer was B but it is saying the answer is C. Am I missing something or is the book wrong?
 

someonesdad

Joined Jul 7, 2009
1,583
In case others don't see the point, the resistance of a piece of wire is

\(R = \rho \frac{L}{A}\)

where ρ is the resistivity of the wire, L is its length, and A is its cross-sectional area. If the wire is round, the area is expressed as the square of the radius.
 
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