Q. 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 ampere. The minimum number of resistances of the type $R$ that will be required for this job
A) 4
B) 10
C) 8
D) 20
Explanation
(c) 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 $= n \times$ (Energy consumed by each resistance)
$\Rightarrow i^{'2}R^{'} = n \times i^{2}R \Rightarrow n = \left( \frac{i^{'}}{i} \right)^{2} \times \left( \frac{R^{'}}{R} \right) = \left( \frac{4}{1} \right)^{2} \times \left( \frac{5}{10} \right) = 8$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.