JEE Main & Advanced Physics Current Electricity, Charging & Discharging Of Capacitors / वर्तमान बिजली, चार्ज और कैपेसिटर का निर Question Bank Critical Thinking

  • question_answer
    Two resistances \[{{R}_{1}}\] and \[{{R}_{2}}\] are made of different materials. The temperature coefficient of the material of \[{{R}_{1}}\] is \[\alpha \] and of the material of \[{{R}_{2}}\] is \[-\beta \]. The resistance of the series combination of \[{{R}_{1}}\] and \[{{R}_{2}}\] will not change with temperature, if \[{{R}_{1}}/{{R}_{2}}\] equals                                                                         [MP PMT 1997]

    A)            \[\frac{\alpha }{\beta }\]

    B)            \[\frac{\alpha +\beta }{\alpha -\beta }\]

    C)            \[\frac{{{\alpha }^{2}}+{{\beta }^{2}}}{\alpha \beta }\]       

    D)            \[\frac{\beta }{\alpha }\]

    Correct Answer: D

    Solution :

                       \[{{R}_{1}}+{{R}_{2}}={{R}_{1}}(1+\alpha t)+{{R}_{2}}(1-\beta \,t)\] Þ \[{{R}_{1}}+{{R}_{2}}={{R}_{1}}+{{R}_{2}}+{{R}_{1}}\alpha t-{{R}_{2}}\beta t\]Þ \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{\beta }{\alpha }\]


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