A) 1154 K
B) 1100 K
C) 1400 K
D) 1127 K
Correct Answer: C
Solution :
The resistance \[{{R}_{t}}\] of a metal conductor at temperature \[{{t}^{o}}C\] is given by \[{{R}_{t}}={{R}_{0}}(1+\alpha t+\beta {{t}^{2}})\] where \[\alpha \] and \[\beta \] are temperature coefficients of resistance. rq is the resistance of conductor at \[{{0}^{o}}C\]. Their values vary from metal to metal. If the temperature \[{{t}^{o}}C\] is not sufficiently large which is so in the most practical cases, the above relation may be expressed as \[{{R}_{t}}={{R}_{0}}(1+\alpha t)\] ??..(i) Given, \[\alpha =0.00125/K\] \[{{R}_{300}}=1\Omega \] From Eq. (i), we have \[1={{R}_{0}}(1+0.00125\times 300)\] ??(ii) and, \[2={{R}_{0}}(1+0.00125\times T)\] ...(iii) \[\therefore \] \[\frac{2}{1}=\frac{1+0.00125\times T}{1+0.00125\times 300}\] or \[2.75=1+0.00125\times T\] or \[T=\frac{1.75}{0.00125}\] \[=1400K\]
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