Question

A silver wire has a temperature coefficient of resistivity $4\times 10^{-3}{}^{\circ }{C}^{-1}$ and its resistance at $20{}^{\circ }C$ is $10\Omega$ . Neglecting any change in dimensions due to the change in temperature, its resistance at $40{}^{\circ }C$ is

• A. $0.8\Omega$
• B. $1.8\Omega$
• C. $10.8\Omega$
• D. $11.6\Omega$

Answer 1

Answer: (C)

Given, $\alpha =4\times 10^{-3}{}^{\circ }{C}^{-1}$
$T_1=20^{\circ }C$
$T_2=40^{\circ }C$
$R(t_2)=R(t_1)(1+a\Delta t)$
$\Delta T=40-20=20^{\circ }C$
$R(t_1)=10\Omega$
$R(40^{\circ }C)=10(1+4\times {\left(10\right)}^{-3}\times 20)\Omega$
$=10\left[1+80\times 10^{-3}\right]$
$=10\left[1.08\right]=10.8\Omega$