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 raisied by ΔT in a time t. A number N of similar cells is now connected in series with a wire of the same material and $$cross-section$$ but the 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 the current, the temperature of the wire is raisied by ΔT in a time t. A number N of similar cells is now connected in series with a wire of the same material and $$cross-section$$ but the 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

In the first case, three identical cells are connected in seires with a wire of length L. Let the terminal potential difference of each cell is V and resistance of the wire is R. Then heat developed in the wire in time t $$isH=(3V)2Rt=ms$$ΔTwhere m is the mass of the wire, $$s-the$$ specific heat of its material and ΔT is the rise in its temperature.When N such identical cells are connected in series, the effective terminal potential is NV volt and if the length of the wire is doubled, its resistance and mass also doubled. Then heat develop in the wire $$isH=(NV)22Rt=(2m)s$$.ΔTDividing both the equations, we $$getN22$$×$$9=2$$⇒$$N=6$$

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