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, $\alpha =4\times 10^{- 3} \, ^\circ C^{- 1}$
$T_{1}=20^\circ C$
$T_{2}=40^\circ C$
$R \left(\right. t_{2} \left.\right) = R \left(\right. t_{1} \left.\right) \left(\right. 1 + a \Delta t \left.\right)$
$\Delta T=40-20=20^\circ C$
$R\left(\right. t_{1} \left.\right)=10\Omega$
$R\left(\right. 40 ^\circ C \left.\right)=10\left(\right. 1 + 4 \times \left(10\right)^{- 3} \times 20 \left.\right)\Omega$
$=10\left[1 + 80 \times 10^{- 3}\right]$
$=10\left[1.08\right]=10.8\Omega$