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
AIPMT 1990, Medium
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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)
$⇒$ $i{'^2}R' = n \times {i^2}R$$⇒$ $n = {\left( {\frac{{i'}}{i}} \right)^2} \times \left( {\frac{{R'}}{R}} \right) = {\left( {\frac{4}{1}} \right)^2} \times \left( {\frac{5}{{10}}} \right) = 8$
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