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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2000

  • question_answer
    The resistance of a conductor is 5 ohm at\[50{{\,}^{o}}C\]  and 6 ohm at \[100{{\,}^{o}}C.\] Its resistance at \[0{{\,}^{o}}C\]is:

    A) 1 ohm                                  

    B)  2 ohm

    C)  3 ohm                                 

    D)  4 ohm

    Correct Answer: D

    Solution :

     From the formula \[R={{R}_{0}}(1+\alpha t)\] Ist case at\[\text{50}{{\,}^{\text{o}}}\text{C,}\] we have                 \[5\,=\,{{R}_{0}}(1+50\,\alpha )\]                             ?(1) lInd case at \[100{{\,}^{o}}C,\] we have                 \[6={{R}_{0}}(1+100\,\alpha )\]                 ?(2) Now dividing equation (2) by equation (1), we get                                 \[\frac{6}{5}=\frac{1+100\alpha }{1+50\alpha }\] \[6+300\alpha =5+500\alpha \]                 so           \[\alpha =\frac{1}{200}\] Again after putting the value of a in equation (1), we get                                 \[5={{R}_{0}}\left( 1+50\times \frac{1}{200} \right)\]                                 \[{{R}_{0}}=\frac{20}{5}=4\,\text{ohm}\]


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