A) \[50\times {{10}^{-8}}\]
B) \[90\times {{10}^{-8}}\]
C) \[100\,\times \,{{10}^{-8}}\]
D) \[200\times {{10}^{-8}}\]
Correct Answer: C
Solution :
Given: Temperature difference \[{{t}_{2}}-{{t}_{1}}=50{{\,}^{o}}C\] And resistivity difference \[{{\rho }_{t}}-{{\rho }_{0}}=2\times {{10}^{-8}}\Omega -m\] and \[\alpha =0.0004/K\] \[{{\rho }_{t}}={{\rho }_{0}}[1+\alpha ({{t}_{2}}-{{t}_{1}})]\] \[{{\rho }_{t}}-{{\rho }_{0}}={{\rho }_{0}}\alpha ({{t}_{2}}-{{t}_{1}})\] or \[{{\rho }_{0}}=\frac{{{\rho }_{t}}-{{\rho }_{0}}}{\alpha ({{t}_{2}}-{{t}_{1}})}\] ?(i) Now, putting the given values in Eq. (i) we get \[{{\rho }_{0}}=\frac{2\times {{10}^{-8}}}{4\times {{10}^{-4}}\times 50}\] \[=100\times {{10}^{-8}}\Omega m\]
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