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A 6 m long wire has diameter 0.5 mm. Its resistance is 50 Ω. Find the resistivity and conductivity.

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Given : l = 6 m, D = 0.5 mm, 

r = 0.25 mm = 0.25 × 10-3 m, R = 50 Ω

To find : 

i. Resistivity (ρ) 

ii. Conductivity (σ)

Formulae :

Calculation : From formula (i),

= {antilog [log 50 + log 3.142 + 21og 0.25 - log 6]} × 10-6 

= {antilog [ 1.6990 + 0.4972 + 2(1.3979) -0.7782]} × 10-6 

= {antilog [2.1962 + 2 .7958 – 0.7782]} × 10-6 

= {antilog [0.9920 – 0.7782]} × 10-6 

= {antilog [0.2138]} × 10-6 

= 1.636 × 10-6 Ω/m

From formula (ii),

….(Using reciprocal from log table)

= 6.157 × 105 m/Ω

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