Question

The rasistance of a conductor of length 5m and area of cross section 1cm square 10 ohm .The value of Resistivity is​

Answer 1

Answer:

$\boxed{\sf Resistivity = 2 \times 10^{-4} \ \Omega -m}$

Given:

Length (l) = 5 m

Area of cross-section (A) = 1 cm² = $\sf 1 \times 10^{-4} \ m^{2}$

Resistance (R) = 10 ohm

Explanation:

$\sf Resistance \propto Length$

$\sf Resistance \propto \frac{1}{Area \ of \ cross-section}$

$\sf \implies Resistance \propto \frac{Length}{Area \ of \ cross-section} \\ \\ \sf \implies Resistance = \rho (\frac{Length}{Area \ of \ cross-section} )\\ \\ \sf \implies R = \rho \frac{l}{A}$

The constant of proportionality $\rho$ is known as resistivity or specific resistance.

$\sf \implies R = \rho \frac{l}{A} \\ \\ \sf \implies \rho \frac{l}{A} = R \\ \\ \sf \implies \rho = R(\frac{A}{l}) \\ \\ \sf \implies \rho = 10 \times \frac{1 \times 10^{-4}}{5} \\ \\ \sf \implies \rho = 2 \times \cancel{5} \times \frac{10^{-4}}{\cancel{5}} \\ \\ \sf \implies \rho = 2 \times 10^{-4} \ \Omega -m$

Additional information:

• Resistivity $(\rho)$ depends on material of the conductor but not on its dimensions

• Resistance (R) depends on both dimension and material of conductor.

Answer 2

Answer:

$\boxed{\sf Resistivity = 2 \times 10^{-4} \ \Omega -m}$

Given:

Length (l) = 5 m

Area of cross-section (A) = 1 cm² = $\sf 1 \times 10^{-4} \ m^{2}$

Resistance (R) = 10 ohm

Explanation:

$\sf Resistance \propto Length$

$\sf Resistance \propto \frac{1}{Area \ of \ cross-section}$

$\sf \implies Resistance \propto \frac{Length}{Area \ of \ cross-section} \\ \\ \sf \implies Resistance = \rho (\frac{Length}{Area \ of \ cross-section} )\\ \\ \sf \implies R = \rho \frac{l}{A}$

The constant of proportionality $\rho$ is known as resistivity or specific resistance.

$\sf \implies R = \rho \frac{l}{A} \\ \\ \sf \implies \rho \frac{l}{A} = R \\ \\ \sf \implies \rho = R(\frac{A}{l}) \\ \\ \sf \implies \rho = 10 \times \frac{1 \times 10^{-4}}{5} \\ \\ \sf \implies \rho = 2 \times \cancel{5} \times \frac{10^{-4}}{\cancel{5}} \\ \\ \sf \implies \rho = 2 \times 10^{-4} \ \Omega -m$

Additional information:

• Resistivity $(\rho)$ depends on material of the conductor but not on its dimensions

• Resistance (R) depends on both dimension and material of conductor.