Question

If resistance of a wire is 26 ohm at 20*c, and its radius is 1.5 mm. Find its resistivity.​

Answer 1

Given: Resistance of a wire is 26 ohm at 20°c, and its radius is 1.5 mm .

Need to Find : Resistivity of the wire .

Here, length of wire is not given so we will 1 m length of the wire .

Conversion of Unit

↠ Radius = 1.5 × 10⁻³ m

Calculating the Area of Cross Section

↠Area of Cross Section = πr²

Area of Cross Section = 3.14 × (1.5×10⁻³)²

↠Area of Cross Section = 7.065 × 10⁻⁶ m²

Now, calculating the resistivity of the wire .

$\\ \star{\boxed{\purple{\bf{\rho = \frac{R\times A}{l} \ }}}}$

On substituting the value we get

$\: \: \: \: \implies \tt \rho \: = \frac{26 \times 7.065 \times {10}^{ - 6} }{1} \: \: \\ \\ \implies \tt \rho \: = 1.83 \times {10}^{ - 4} ohm \: metre$

• Hence, the resistivity of the wire is 1.83 × 10⁻⁴ Ω m .

Answer 2

Given: Resistance of a wire is 26 ohm at 20°c, and its radius is 1.5 mm .

Need to Find : Resistivity of the wire .

Here, length of wire is not given so we will 1 m length of the wire .

Conversion of Unit

↠ Radius = 1.5 × 10⁻³ m

Calculating the Area of Cross Section

↠Area of Cross Section = πr²

Area of Cross Section = 3.14 × (1.5×10⁻³)²

↠Area of Cross Section = 7.065 × 10⁻⁶ m²

Now, calculating the resistivity of the wire.

$\large \blue{\underline{ \green{\boxed{\bf{ \red{ \rho = \frac{R \times A}{l} }}}}}}$

On substituting the values we get:-

$\large{\sf{ \implies \rho = \frac{26 \times 7.065 \times {10}^{ - 6} }{1} }}$

$\large{\sf{ \implies \rho = 1.83 \times {10}^{ - 4} ohm \: metre}}$

$\small{\bf{Hence,the \: resistivity \: of \: the \: wire}}$

$\small{\bf{is \: 1.83 \times {10}^{ - 4} Ω \: m}}$