Apply the definition of electric resistance to solve all the problems. 1. A copp

Question

Apply the definition of electric resistance to solve all the problems. 1. A copper wire has a circular cross-section with diameter 2.053-mm. (a) Calculate the cross-sectional area of this wire, in m2. (b) Calculate the resistance of a 20.0-m-long piece this wire. 2. A tungsten filament has a circular cross-section with diameter 0.100-mm (a) Calculate the cross-sectional area of this filament, in m2. at 20.0°c, calculate how long it should be. b) If the tungsten filament is to have a resistance of 0.200 0 3. Determine of what material is a wire made, if it is 25.0 m long with a 0.100-mm cross-section diameter and a resistance of 77.7 at 20.0°C

Explanation / Answer

1. (A) A = pi r^2 = pi D^2 / 4

A = pi (2.053 x 10^-3)^2 / 4

A = 3.31 x 10^-6 m^2  

(B) R = rho L / A

for copper, rho = 1.72 x 10^-8 ohm m

R = (1.72 x 10^-8 ohm m)(20 m) / (3.31 x 10^-6 m^2)

R = 0.104 Ohm  

2. (a) A = pi D^2 /4 = 7.854 x 10^-9 m^2  

(b) R = rho L / A

0.200 = (5.6 x 10^-8) (L) / (7.854 x 10^-9)  

L = 0.028 m

3. 77.7 = (rho) (25) / (pi (0.100 x 10^-3)^2 / 4)

rho = 2.44 x 10^-8 ohm m

material is Gold.

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