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

Question

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 : [2024]

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(3)

Given, $R_{0} = 8 Ω$ and $R_{100} = 10 Ω$

$∴$ $R_{100} = R_{0} (1 + α ∆ T)$

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

Also, $R_{400} = R_{0} (1 + α ∆ T)$

$∴$ $R_{400} = 8 (1 + 400 α) = 8 (1 + 1) = 16 Ω$

Solution

Q.
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 : [2024]

1 $8 Ω$

2 $10 Ω$

3 $16 Ω$

4 $2 Ω$

Ans.
(3)

Given, $R_{0} = 8 Ω$ and $R_{100} = 10 Ω$

   $∴$ $R_{100} = R_{0} (1 + α ∆ T)$

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

Also, $R_{400} = R_{0} (1 + α ∆ T)$

$∴$    $R_{400} = 8 (1 + 400 α) = 8 (1 + 1) = 16 Ω$

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Solution

Q. The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are 8Ω and 10Ω respectively. After inserting in a hot bath of temperature 400°C, the resistance of platinum wire is : [2024]

1 8Ω

2 10Ω

3 16Ω

4 2Ω

Ans. (3) Given, R0=8Ω and R100=10Ω ∴ R100=R0(1+α∆T) ∴ 10=8(1+α×100)⇒100α=14 Also, R400=R0(1+α∆T) ∴ R400=8(1+400α)=8(1+1)=16Ω