Question

Calculate the resistance of 180 m of silver wire having a cross section of 033mm^2. The resistivity of silver is 16×10−8Ωm

a. 112Ω

b. 96Ω

c. 146Ω

d. 75Ω

Answer 1

Calculate the resistance of 180 m of silver wire having a cross section of 0.33 mm². The resistivity of silver is 1.6×10⁻⁸ Ω m

a. 112 Ω

b. 96 Ω

c. 146 Ω

d. 75 Ω

The resistance of a given object depends primarily on two factors: What material it is made of, and its shape. For a given material, the resistance is inversely proportional to the cross-sectional area. Also, for a given material, the resistance is proportional to the length. The resistance R and conductance G of a conductor of uniform cross section, therefore, can be computed as:

$$R = \frac {\rho l}{S}$$

where ρ – resistivity of material, l – length, S – cross section.

Therefore:

$$R = \frac {1.6 \times 10^{-8} \Omega \, \text{m} \times 180 \, \text{m}}{0.33 \, \text{mm}^2} = 8.72 \, \Omega$$

Answer: R = 8.72 Ω