Question

5.
The resistance of a resistance thermometer has
values 2.71 and 3.70 ohm at 10°C and 100°C. The
temperature at which the resistance is 3.26 ohm is
(a) 40°C
(b) 50°C
(c) 60°C
(d) 70°C


with explanation ​

Answer 1

$\huge\underline{\underline{\bf \green{Question-}}}$

The resistance of a resistance thermometer has

values 2.71 and 3.70 ohm at 10°C and 100°C. The

temperature at which the resistance is 3.26 ohm is -

$\huge\underline{\underline{\bf \green{Solution-}}}$

$\large\underline{\underline{\sf Given:}}$

• ${\sf R_1=2.71\:Ω}$
• ${\sf R_2=3.70\:Ω}$
• ${\sf T_1=10°C}$
• ${\sf T_2=100°C}$
• Resistance ( R ) = 3.26 Ω

$\large\underline{\underline{\sf To\:Find:}}$

• The temperature at which the resistance is 3.26 ohm ( T )

Change in resistance (∆R) = 3.70 - 2.71

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 0.99 Ω

Change in Temperature (∆T) = 100 - 90

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 10°C

Change in new Resistance

➝ 3.26 - 2.71

➝ 0.55 Ω

Hence ,

❏ Change in Temperature ➝

$\implies{\sf \dfrac{90}{0.99}×0.55 }$

$\implies{\bf \red{50°C} }$

$\huge\underline{\underline{\bf \green{Answer-}}}$

Option ( b ) 50°C

The temperature at which the resistance is 3.26 ohm is ${\bf \red{50°C}}$

Answer 2

$\huge{\bold{\red{\star{\pink{Heya!}}}}}$

Option[B] 50°C is the answer ✔️