A coil has resistance of 18 when its mean temperature is 20°C and of 20 when its mean temperature is 50°C. What will be mean temperature rise when its resistance is 21 2 and the surrounding temperature is 15°C.
Answer & explanation
Correct answer: option 2
$ 18 = R_0 (1+ 20 \alpha )$
$ 20 = R_0 (1+ 50 \alpha )$
Dividing these two
$\Rightarrow \frac{18}{20} = \frac{1+ 20 \alpha}{1+ 50 \alpha}$
$ \alpha = \frac{1}{250}$
$\text{Let Resistance become }21\Omega \text{ when temperature is t}$
$\Rightarrow 21 = R_0 (1+\alpha t)$ = R0 (1+t/250)
$\text{Divide this to equation 1 }$
$\Rightarrow \frac{21}{18} = \frac{1+t/250}{1+20/250}$
$\Rightarrow t = 65^oC$
$\text{Rise in Temperature } = 65^oC - 15^oC= 50^oC$