Question

Resistance of a conductor of lent 1 m and cross-sectional area of 1 mm² is eight ohm find the specific a resistance of the conductor

Answer 1

Answer :

Length of conductor = 1m

Area of cross section = 1mm² = $10^{-6}$m²

Resistance of conductor = 8Ω

We have to find specific resistance (resistivity) of conductor.

Resistance of conductor is directly proportional to the length of conductor and inversely proportional to the area of cross section.

• R ∝ L / A

Here, ρ is the proportionality constant which denotes resistivity of conductor.

⇒ R = ρ × (L / A)

⇒ ρ = R × (A / L)

⇒ $\bf{\rho = 8\times 10^{-6}\:\Omega m}$

☃ God_Bless :)

Answer 2

$\huge\sf\pink{Answer}$

☞ Your Answer is 8 × $\sf 10^{-6}$ Ωm

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$\huge\sf\blue{Given}$

✭ Length of conductor = 1 m

✭ Cross section area = 1 mm² = $\sf 10^{-6}$ m²

✭ Resistance = 8Ω

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$\huge\sf\gray{To \:Find}$

◈ The resistivity of the conductor?

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$\huge\sf\purple{Steps}$

So here we shall use the formula,

$\underline{\boxed{\sf R = \rho \dfrac{L}{A}}}$

Where

◕ R = Resistance

◕ L = Length of the conductor

◕ A = Cross sectional area of the conductor

◕ ρ = Proportionality constant denoting Resistivity

So on substituting the given values,

➝ $\sf R = \rho \dfrac{L}{A}$

➝ $\sf \rho = R \dfrac{A}{L}$

➝ $\sf \rho = 8\dfrac{10^{-6}}{1}$

➝ $\sf \orange{\rho = 8\times 10^{-6} \ \Omega m}$

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