The resistance of a conductor at 15°C

Question:

The resistance of a conductor at $15^{\circ} \mathrm{C}$ is $16 \Omega$ and at $100^{\circ} \mathrm{C}$ is $20 \Omega$. What will be the temperature coefficient of resistance of the conductor?

  1. $0.010^{\circ} \mathrm{C}^{-1}$

  2. $0.033^{\circ} \mathrm{C}^{-1}$

  3. $0.003^{\circ} \mathrm{C}^{-1}$

  4. $0.042^{\circ} \mathrm{C}^{-1}$


Correct Option: , 3

Solution:

$16=\mathrm{R}_{0}\left[1+\alpha\left(15-\mathrm{T}_{\mathrm{o}}\right)\right]$

$20=\mathrm{R}_{0}\left[1+\alpha\left(100-\mathrm{T}_{\mathrm{o}}\right)\right]$

Assuming $\mathrm{T}_{0}=0^{\circ} \mathrm{C}$, as a general convention.

$\Rightarrow \frac{16}{20}=\frac{1+\alpha \times 15}{1+\alpha \times 100}$

$\Rightarrow \alpha=0.003{ }^{\circ} \mathrm{C}^{-1}$

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