You need to prepare a 0.199-mm-diameter tungsten wire with a resistance of 3.09 kÏ. how long must the wire be? the resistivity of tungsten is 5.62 à 10-8 Ï·m.
1.71x10^3 meters.
The resistivity of a conductor with an uniform cross section is expressed as
R = pl/A
where
p = resistivity
l = length of conductor
A = cross sectional area of conductor.
Solving for l gives
R = pl/A
RA = pl
RA/p = l
The cross section is defined a A = pi r^2, so
A = 3.14159 * (9.95x10^-5 m)^2
A = 3.14159 * 9.90025x10^-9 m^2
A = 3.11025x10^-8 m^2
Now substitute the known values into the formula, giving:
RA/p = l
3090 ohm * 3.11025x10^-8 m^2 / 5.62x10^-8 ohm * m = l 1.71009x10^3 m
Rounding to 3 significant places gives 1.71x10^3 meters.
