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JCECE Engineering JCECE Engineering Solved Paper-2014

  • question_answer
    The values of two resistors are \[{{R}_{1}}=(6+0.3)k\Omega \] and\[{{R}_{2}}=(10\pm 0.2)k\Omega \]. The percentage error in the equivalent resistance when, they are connected in parallel is

    A) \[5.125%\]                         

    B) \[2%\]

    C) \[10.125%\]                       

    D) \[7%\]

    Correct Answer: C

    Solution :

                    \[{{R}_{p}}=\frac{{{R}_{1}}{{R}_{2}}}{{{R}_{1}}+{{R}_{2}}}\]                 \[\frac{\Delta {{R}_{p}}}{{{R}_{p}}}=\frac{\Delta {{R}_{1}}}{{{R}_{1}}}+\frac{\Delta {{R}_{2}}}{{{R}_{2}}}+\frac{\Delta ({{R}_{1}}+{{R}_{2}})}{{{R}_{1}}+{{R}_{2}}}\]                 \[\frac{\Delta {{R}_{p}}}{{{R}_{p}}}=\frac{0.3}{6}+\frac{0.2}{10}+\frac{0.3+0.2}{1.16}\]                 \[=\frac{\Delta {{R}_{p}}}{{{R}_{p}}}\times 100\]                 \[=10.125%\]


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