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Physics · 2024 · 3 marks
CBSE 2024 · Region 5 · Set 2 · Q24
(i) Define 'temperature coefficient of resistance' of a metal. (ii) Show the variation of resistivity of copper with rise in temperature. (iii) The…
(i)
Define 'temperature coefficient of resistance' of a metal.
(ii)
Show the variation of resistivity of copper with rise in temperature.
(iii)
The resistance of a wire is $\displaystyle 10 \Omega$ at $\displaystyle 27{ }^{\circ} \mathrm{C}$. Find its resistance at $\displaystyle -73{ }^{\circ} \mathrm{C}$. The temperature coefficient of resistance of the material of the wire is $\displaystyle 1.70 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}$.
Marking-scheme solution
(i)
Change in resistance per unit original resistance per degree change in temperature is the temperature coefficient of resistance.
(iii)
$\displaystyle R_{2}=R_{1}\left(\theta_{2}-\theta_{1}\right) \alpha+R_{1}$
$\displaystyle =10(-73-27) \times 1.70 \times 10^{-4}+10$
$\displaystyle =-0.170+10$
$\displaystyle R_{2}=9.83 \Omega$
$\displaystyle R_{1}=R_{0}\left(1+\alpha t_{1}\right)$
$\displaystyle R_{2}=R_{0}\left(1+\alpha t_{2}\right)$
$\displaystyle \frac{R_{1}}{R_{2}}=\frac{\left(1+\alpha t_{1}\right)}{\left(1+\alpha t_{2}\right)}$
$\displaystyle R_{2}=\frac{\left(1+\alpha t_{2}\right)}{\left(1+\alpha t_{1}\right)} R_{1}$
$\displaystyle R_{2}=\frac{\left[1+1.70 \times 10^{-4} \times(-73)\right]}{\left[1+1.70 \times 10^{-4} \times 27\right]} \times 10$
$\displaystyle R_{2}=\frac{0.98759}{1.00459} \times 10 \Omega$
$\displaystyle R_{2}=9.83 \Omega$
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