PYQ NEET- Current Electricity L-5

Question: The resistance of platinum wire at $0^{\circ} \mathrm{C}$ is $2 \Omega$ and $6.8 \Omega$ at $80^{\circ} \mathrm{C}$. The temperature coefficient of resistance of the wire is : (2023)#

A) $3 \times 10^{-3} \mathrm{C}^{-1}$

B) $3 \times 10^{-2} \mathrm{C}^{-1}$

C) $3 \times 10^{-10} \mathrm{C}^{-1}$

D) $3 \times 10^{-4} \mathrm{C}^{-1}$

Answer: $3 \times 10^{-2} \mathrm{C}^{-1}$#

Explanation#

$\mathrm{R}_{\mathrm{T}}=\mathrm{R}_0\left[1+\alpha\left(\mathrm{T}-\mathrm{T}_0\right)\right]$

$6.8=2[1+\alpha(80-\alpha)]$

$\alpha=\frac{2.4}{80}=0.03 /{ }^{\circ} \mathrm{C}=3 \times 10^{-2} /{ }^{\circ} \mathrm{C}$