Question

The resistance of a wire of length 100cm and of uniform area of cross- section 0.030 cm2 , is found to be 1.5 Ω. Calculate the resistivity of the wire.

Answer 1

$\color{darkblue}\underline{\underline{\sf Given-}}$

• Resistance of wire (R) = 1.5Ω
• Lenght of wire $(\ell)$ = 100cm or ${\sf 1m}$
• Area of cross section (A) = ${\sf 0.03×10^{-4}m}$

$\color{darkblue}\underline{\underline{\sf To \: Find -}}$

• Resistivity $(\rho)$

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★$\underline{\sf Formula \: used -}$

$\color{violet}\bullet\underline{\boxed{\sf R=\rho\dfrac{\ell}{A}}}$

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$\color{darkblue}\underline{\underline{\sf Solution-}}$

$\implies{\sf 1.5=\rho\dfrac{1}{0.03×10^{-4}} }$

$\implies{\sf 1.5=\rho\dfrac{1}{3×10^{-6}}}$

$\implies{\sf \rho = 1.5×3×10^{-6} }$

$\color{red}\implies{\sf \rho = 4.5×10^{-6}Ω.m}$

$\color{darkblue}\underline{\underline{\sf Answer-}}$

★Resistivity of wire is $\color{red}{\sf 4.5×10^{-6}Ω.m}$

Answer 2

$\mathtt{\huge{ \fbox{Solution :)}}}$

Given ,

• Length of the wire = 100 cm
• Area of the cross section of wire = 0.030 cm²
• Resistance of the wire = 1.5 Ω

We know that ,

The resistance of the wire is

(i) directly proportional to the length of the wire

(ii) inversely proportional to the area of the cross section of the wire

$\mathtt{ \fbox{R = Resistivity \times \frac{length}{area} }}$

Thus ,

Resistivity = (1.5 × 0.030)/100

Resistivity = (15 × 30)/(10)^6

Resistivity = 45 × (10)^-5 Ω m

Hence , the resistivity is 45 × (10)^-5 Ω m

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