A) \[{{0.0012}^{o}}{{C}^{-1}}\]
B) \[{{0.0024}^{o}}{{C}^{-1}}\]
C) \[{{0.0032}^{o}}{{C}^{-1}}\]
D) \[{{0.0064}^{o}}{{C}^{-1}}\]
Correct Answer: D
Solution :
If the resistance of wire at \[{{0}^{o}}C\] be \[{{R}_{0}}\] and at \[{{t}^{o}}C\] be \[{{R}_{t}}\], then the value of \[{{R}_{t}}\] will be obtained from the following formula \[{{R}_{t}}={{R}_{0}}\,(1+\alpha \,\,t)\] where \[\alpha \] is a constant called temperature coefficient of resistance. \[\Rightarrow \] \[\alpha =\frac{{{R}_{t}}-{{T}_{0}}}{{{R}_{0}}\,t}{{/}^{o}}C\] Putting the numerical values, we have \[\alpha =\frac{4.5-3.1}{3.1\times (100-30)}\] \[=\frac{1.4}{3.1\times 70}\] \[=\frac{1.4}{217}={{0.0064}^{o}}{{C}^{-1}}\]
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