Question

Resistance of metal wire of length 2m is 20 ohm at 30 degree celsius . if the radius of the wire is 0.15 mm . find the resistivity of that metal

Answer 1

Explanation:

Given,

Resistance = 20ohm;

length = 2 m;

radius of wire = 0.15 mm or 1.5 × 10^-4;

Now, area of the wire =

$\pi {r}^{2}$

Hence, area = 22/ 7 × (1.5 × 10^-4)^2;

= 22 / 7 × (2.25 × 10^-8);

=(22×2.25×10^-8) / 7;

Now, we have a relation between yhe given things and that relation is ;

R = rho ×(l/A)

where, R is resistance

rho = resistivity

l = length

A = area

Hence put the variables in the formula;

20 ohm = rho {2 / (22 × 2.25×10^-8) /7}

20ohm = rho {(2×7) / (22 × 2.25 × 10^-8)};

= rho {(14 × 10^8) / 22 × 2.25};

rho = {20 × (22 × 2.25)} / (14× 10^8);

= (990×10^-8)/14

= (495× 10^-8) / 7;

=(4.95×10^-6)/7 ohm . m;

That's all.