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

Infinity Learn · Accepted Answer

We know that heat $$developed=i2$$ R t. $$Hence3ER12R1t=m1sdtand$$ $$NER22R2t=m2sdt$$∴ $$N29=m2m1$$×$$R2R1or$$ $$N2=9m2m1R2R1N=3m2m1R2R1=32m1m12R1R1=6$$

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