Question

resistance of a metal wire of length 2 m is 30 ohm at temperature 25 degreecalcius

Answer 1

$\huge \bf{Question}$

Resistance of a metal wire of length 2 m is 30

Ω at temperature 25° C. If the diameter of the

wire is 0.6 mm, then what will be the resistivity

of the metal at that temperature?

$\huge \bf Solution$

Given,

$\bf \: Length \: of \: wire ,\: l = 2 \: m$

Resistance, R = 30 Ω, Temperature, T = 25° C

Diameter of wire, d = 0.6 mm = 6 × 10⁻⁴

Resistivity of the wire, ρ = ?

$\bf \: We \: know \: that,$

$\bf \: ρ \: = \: \frac{RA}{l} \: = \: \frac{R\pi \: d {}^{2} }{4 \: l}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bigg[ \because \: \bf \: A \: = \: \frac{\pi \: d {}^{2} }{4} \bigg]$

$\: \: \bf = \: \frac{30 \times \pi \times (6 \times 10 { }^{ - 4} ) {}^{2}}{4 \times 2}$

$= \: \bf\:4.24 \times 10 {}^{ - 6} \: Ω\: - m$

The resistivity of the metal at 25° C is

4.24 × 10⁻⁶ Ω-m