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

  • question_answer
    You are given several identical resistances each of value \[R=10\,\Omega \] and each capable of carrying maximum current of 1 ampere. It is required to make a suitable combination of these resistances to produce a resistance of \[5\,\Omega \] which can carry a current of 4 amperes. The minimum number of resistances of the type \[R\] that will be required for this job [CBSE PMT 1990]

    A)            4    

    B)            10

    C)            8    

    D)            20

    Correct Answer: C

    Solution :

                       Suppose n resistors are used for the required job. Suppose equivalent resistance of the combination is R' and according to energy conservation it's current rating is \[i'.\] Energy consumed by the combination = n ´ (Energy consumed by each resistance) Þ \[i{{'}^{2}}R'=n\times {{i}^{2}}R\]Þ \[n={{\left( \frac{i'}{i} \right)}^{2}}\times \left( \frac{R'}{R} \right)={{\left( \frac{4}{1} \right)}^{2}}\times \left( \frac{5}{10} \right)=8\]


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