A wire of length L and $$3$$ identical cells of negligible internal resistances are connected in series. Due to current, the temperature of the wire is raised by ΔT in time t. A number N of similar cells is now connected in series with a wire of the same material and $$cross-sectionbut$$ of length $$2L$$.The temperature of the wire is raised by the same amount ΔT in the same time t. The value of N is

Question

A wire of length L and $$3$$ identical cells of negligible internal resistances are connected in series. Due to current, the temperature of the wire is raised by ΔT in time t. A number N of similar cells is now connected in series with a wire of the same material and $$cross-sectionbut$$ of length $$2L$$.The temperature of the wire is raised by the same amount ΔT in the same time t. The value of N is

Infinity Learn · Accepted Answer

Let R and m be the resistance and mass of the first wire, then the second wire has resistance $$2R$$ and mass $$2m$$. Let E $$=$$ emf of each cell, S $$=$$ specific heat capacity of the material of the wire. For the first wire, current $$i1$$ $$=$$ $$3ER$$  and  $$i12$$  Rt  $$=$$  mSΔTFor the second wire, $$i2$$ $$=$$ NER and   $$i12$$  $$2Rt$$  $$=$$ $$2$$ mSΔT.Thus, $$i1$$  $$=$$  $$i2$$  or  $$N=6$$.

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