does the resistance double as you double the length of a
piece of wire?
Is this a trick question? Seems like it might be... Yes, the resistance is
proportional to the length. Therefore if the length is doubled, the
resistance is doubled. Interestingly, the relationship of resistance to
diameter is not so simple and the frequency of the current affects the
resistance (actually, the impedance... have you met this term?).
Yes, the resistance of a wire is directly proportional to the length and
inversely proportional to the Area. Hence doubling the length of a wire
increases the resistance by a factor of two, doubling the area would
decrease the resistance by half. The proportionality constant relating
resistance to the length and area of a wire is the resistivity of the wire.
Resistance=Resistivity x length/area
The resistance of a wire, under nearly constant temperature conditions, is
directly proportional to length and inversely proportional to the cross
R = (rho)L/A
R is the resistance
rho is the characteristic of the material, and is a measured
quantity. Copper has a different
rho than say, carbon.
L is the length of the wire
A is the effective cross sectional area of the wire.
Most introductory college physics texts have more information about this.
---Nathan A. Unterman
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Update: June 2012