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

Question

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

Infinity Learn · Accepted Answer

$$V2Rt=ms($$Δ$$T)$$⇒$$V2At$$ρ$$L=dAL($$Δ$$T)$$⇒ $$V2L2=ds$$ρ$$($$Δ$$T)t=constant$$⇒ $$(3E)2L2=(NE)2(2L)2$$⇒$$N2=36$$ ⇒ $$N=6$$

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