Question

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.

Answer 1

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.