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# 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 $\Delta T$ in a time $t$. A number $N$ of similar cells are now connected in series with a wire of the same material and cross-section but of length $2L$. The temperature is raised by the same amount $\Delta T$ in the same time. The value of $N$ is

$\begin {array} {1 1} (A)\;4 \\ (B)\;6 \\ (C)\;Non-integral\: answer. \: The \: described\: situation\: is\: not \: possible \\ (D)\;None \: of \: these \end {array}$

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## 1 Answer

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In the first case, $(3E)^2 \large\frac{t}{R}$ $=ms \Delta T$
In the second case, $( NE)^2 \large\frac{t}{2R}$ $= (2m) s \Delta T$
Note here that as the length is doubled, the resistance and the mass, both are doubled.
Solving the equations give $N = 6.$
One gets non-integer answers if the effect of mass is not taken care of.
Ans : (B)
answered Feb 8, 2014
edited Mar 14, 2014

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