You are given several identical resistances each of value R $$=$$ $$10$$Ω 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 $$5$$Ω which can carry a current of $$4$$ amperes. The minimum number of resistances of the type R that will be required for this job

Question

You are given several identical resistances each of value R $$=$$ $$10$$Ω 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 $$5$$Ω  which can carry a current of $$4$$ amperes. The minimum number of resistances of the type  R that will be required for this job

Infinity Learn · Accepted Answer

Suppose n resistors are used for the required job. Suppose equivalent resistance of the combination is R' and according to energy conservation its current rating is  i'.Energy consumed by the combination $$=$$ n x (Energy$$ consumed by each $$resistance)⇒i'$$2R$$′$$=n$$×$$i2R$$⇒$$n=i$$′$$i2$$×R′$$R=412$$×$$510=8$$

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