Question

A silver wire has temperature coefficient of resistivity $4 \times 10^{-3} /{ }^{\circ} C$ 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. $ 9.2 \, \Omega$
• D. $ 10.8 \, \Omega $
• E. $11.6 \, \Omega$

Answer 1

Answer: (D)

Given, $ \alpha=4 \times 10^{-3} /{ }^{\circ} C $
$T_{1} =20^{\circ} C $
$T_{2} =40^{\circ} C $
$R t_{2} =R t_{1}(1+\alpha \Delta t) $
$ \Delta T =40-0=20^{\circ} C $
$R t_{1} =10 \,\Omega $
$R_{4} \Omega =10\left(1+4 \times 10^{-3} \times 20\right] \Omega $
$=10\left[1+80 \times 10^{-3}\right] $
$ =10[1.08]=10.8 \,\Omega $