The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are 8 Ω and 10 Ω respectively. After inserting in a hot bath of temperature 400 ° C , the resistance of platinum wire is :

Physics · Thermal Properties of Matter

JEE Main 2024 — 4 April, Shift 1 — Question 36

The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $8 \Omega$ and $10 \Omega$ respectively. After inserting in a hot bath of temperature $400^{\circ} \mathrm{C}$ , the resistance of platinum wire is :

Option A:
$2 \Omega$
Option B:
$16 \Omega$
Correct
Option C:
$8 \Omega$
Option D:
$10 \Omega$

Answer: B

Step-by-step solution

Given $\mathrm{R}_{0}=8 \Omega, \mathrm{R}_{100}=10 \Omega$

$\therefore \mathrm{R}_{100}=\mathrm{R}_{0}(1+\alpha \Delta \mathrm{T})$

$\text { Also, } \mathrm{R}_{400}=\mathrm{R}_{0}\left(1+\alpha \Delta \mathrm{T}^{1}\right)$

$\therefore 10=8(1+\alpha \times 100) \Rightarrow 100 \alpha=\frac{1}{4}$

$\therefore \mathrm{R}_{400}=8(1+400 \alpha)=8(1+1)=16 \Omega$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 4 April, Shift 1
Subject: Physics
Chapter: Thermal Properties of Matter
Topic: Thermal Expansion of Solids and its Applications

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Answer: B

Step-by-step solution

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