First slide

Electrical power

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

Moderate

A

4
B

6
C

8
D

9

Solution

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 $i_{1} = \frac{3 E}{R} and i_{1}^{2} Rt = mSΔT$
For the second wire, $i_{2} = \frac{NE}{R}$ and $i_{1}^{2} (2 R) t = 2 mSΔT .$
Thus, $i_{1} = i_{2} or N = 6 .$

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