Question

If r = 4 ohm, cross-section area is 1mm^2, and length = 20m. Then find its conductivity?

Answer 1

$\large\underline{\underline{\sf Given:}}$

• Resistance (R) = 4Ω

• Area (A) = 1mm² or $\sf{10^{-3}m}$

• Length (L) = 20m

$\large\underline{\underline{\sf To\:Find:}}$

• Conductivity $\sf{(\sigma)}$=?

$\large\underline{\underline{\sf Solution:}}$

$\large{\boxed{\sf Conductivity (\sigma)=\frac{1}{Resistivity (\rho)}}}$

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$\large{\boxed{\sf Resistance (R)=\rho\frac{L}{A}}}$

$\large\implies{\sf 4=\rho\frac{20}{10^{-3}} }$

$\large\implies{\sf \rho=\frac{4×10^{-3}}{20} }$

$\large\implies{\sf \rho=\frac{10^{-3}}{5} ohm.m}$

Now ,

$\large\implies{\sf Conductivity (\sigma)=\frac{1}{\rho}}$

$\large\implies{\sf \sigma=\frac{5}{10^{-3}} }$

$\large\implies{\sf \sigma=5000\:siemens\:per\:meter}$

$\Large\underline{\underline{\sf Answer:}}$

•°•Conductivity is 5000 Siemens per meter.