Question

A wire of length L and 3 identical cells of negligible internal resistance are connected in series. Due to the current, the temperature of the wire is raised by DeltaT 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 of length 2L. The temperature of the wire is raised by the same amount DeltaT in the same time t. the value of N is

Answer 1

Answer:

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Explanation:

Here a wire of length L and three identical cells of negligible internal resistances are connected in series.

Let, the terminal potential difference of each cell is V and resistance of wire is R.

then heat developed in the wire in time t is

H=(

R

(3V)

2

)=msΔT

where m is the mass of wire

s is the specific heat of its material and

ΔT is rise in its temperature

When N such identical cells are connected in series the effective terminal

potential is NV volts and if the length of wire is doubled its resistance and

mass also doubled then heat developed in the wire is

H=(

2R

(NV)

2

)t=2msΔT

dividing both equations we get

2×9

N

2

=2

∴N=6