Question

At 20°C, the resistance of a silver wire is 30Ω. (Coefficient of temperature=0.0038). (a) If the wire is 1.2m- long, what is the radius of the wire? (b) What is the resistance of the same wire at 10°C? (c) What is the resistivity of the wire at 25°C?

Answer 1

$R=R_0(1+\alpha t)$

(a)

$R=\rho\frac{l}{A} \to A=\rho\frac{l}{R}=1.59\cdot10^{-8}\cdot\frac{1.2}{30}=636\cdot10^{-12}\ (m^2)$

$A=\pi r^2\to \frac{}{}r=\sqrt{\frac{A}{\pi}}=\sqrt{\frac{636\cdot10^{-12}}{3.14}}=1.42\cdot10^{-5}\ (m)$ . Answer

(b)

$R=R_0(1+\alpha t)\to$

$R=R_0(1+0.0038\cdot20)$

$R_{10}=R_0(1+0.0038\cdot10)\to$

$R/R_{10}=(1+0.0038\cdot20)/(1+0.0038\cdot10)$

$30/R_{10}=1.0366\to R_{10}=28.94\ (\Omega)$ . Answer

(c)

$\rho=\rho_0(1+\alpha t)$

$1.59\cdot10^{-8}=\rho_0(1+0.0038\cdot20)$

$\rho_{25}=\rho_0(1+0.0038\cdot25)$

$1.59\cdot10^{-8}/\rho_{25}=\rho_0(1+0.0038\cdot20)/\rho_0(1+0.0038\cdot25)\to$

$1.59\cdot10^{-8}/\rho_{25}=0.9826\to \rho_{25}=1.62\cdot10^{-8}$ . Answer