A) \[\frac{1}{25}{}^\circ {{C}^{-1}}\]
B) \[\frac{1}{50}{}^\circ {{C}^{-1}}\]
C) \[\frac{1}{80}{}^\circ {{C}^{-1}}\]
D) \[\frac{1}{75}{}^\circ {{C}^{-1}}\]
E) \[\frac{1}{40}{{\,}^{\text{o}}}{{C}^{-1}}\]
Correct Answer: D
Solution :
The resistance at temperature t is \[{{R}_{t}}={{R}_{0}}(1+\alpha t)\] \[R_{t}^{}={{R}_{0}}(1+\alpha t)\] \[\Rightarrow \] \[4=1+15\alpha \] ...(1) \[5=1+37.5\alpha \] ...(2) \[\Rightarrow \] \[\frac{4}{5}=\frac{1+15\alpha }{1+37.5\alpha }\] \[\Rightarrow \] \[4(1+37.5\alpha )=5(1+15\alpha )\] \[\Rightarrow \] \[75\alpha =1\] \[\Rightarrow \] \[\alpha =\frac{1}{75}{}^\circ {{C}^{-1}}\]
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