Question

Resistance of a metal wire of length 1 m is 26 12 at 20 C. If the diameter of the wire is 0.3 mm, what will be the resistivity of the metal at that temperature? Using Table 12.2, predict the material of the wire. ​

Answer 1

Explanation:

☘Answer:-

Given:-

• diameter of the wire is 0.3 mm.
• length of the wire 1m.
• temperature of the metal 20°C.

To find:-

• resistivity of the metal at 20° temperature.

Solution:-

$R \: = \: 26Ω$

$I \: = \: 1m$

$d \: = \: 0.3m$

$\: \:$

$r \:⟹ \: \frac{d}{2} \:$

$⟹ \: \frac{0.3 \: \times \: 10 { }^{ - 3} }{2} \:$

$⟹ \: 0.15 \: \times \: 10 { }^{ - 3}$

$A \: = \: \pi \: r {}^{2}$

$⟹ \: 3.14 \: \times \: (0.15 \: \times \: 10 {}^{ - 3} ) {}^{2}$

$⟹ \: 0.071 \: \times \: 10 {}^{ - 6} m {}^{2}$

$R \: = \: \frac{ρL}{A}$

$or \: ρ \: = \: \frac{RA}{I } \:$

$⟹ \: \frac{26 \: \times \: 0.071 \: \times \: 10 {}^{ - 6} }{1}$

$⟹ \: 1.84 \: \times \: 10 {}^{ - 6} Ωm$

‌‌‎

${\tt ⭐Resistivity \: \: of \: \: the \: \: metal \: \: at \: \: 20° \: temperature }$

‌‌‎

$\boxed {\tt ☆ 1.84 \: \times \: 10 {}^{ - 6} Ωm ☆}$