A wire of length L and 3 identical cells of negligible internal resistances are

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A wire of length L and 3 identical cells of negligible internal resistances are connected in series. Due to this 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 wire is raised by same amount

Δ T

in the same time t. The value of N is

Options:

A . 4

B . 6

C . 8

D . 9

Answer: Option B
:
B
Heat

= m S Δ T = i^{2} R t

Case I: Length (L)

\Rightarrow

Resistance = R and mass = m
Case II: Length (2L)

\Rightarrow

Resistance = 2R and mass = 2m
So

\frac{m_{1} S_{1} Δ T_{1}}{m_{2} S_{2} Δ T_{2}} = \frac{i_{1}^{2} R_{1} t_{1}}{i_{2}^{2} R_{2} t_{2}} \Rightarrow \frac{m S Δ T}{2 m S Δ T} = \frac{i_{1}^{2} R t}{i_{2}^{2} 2 R t} \Rightarrow i_{1} = i_{2} \Rightarrow \frac{(3 E)}{R} = \frac{(N E)}{2 R} \Rightarrow N = 6

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