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  • A wire of length  and 3 identical cells of negligible resistances are connected in seri

A wire of length2 \mathrm{~m}  and 3 identical cells of negligible resistances are connected in series. Due to the current, the temp of wire raise by \Delta T in time t. A number of N similar cells is now connected in series with wire of same material and cross section but of length 4 \mathrm{m}. The temp. of wire raised by same amount \Delta T in the same time t. The value of N is:-

Option: 1

7


Option: 2

4


Option: 3

5


Option: 4

6


Answers (1)

best_answer

\begin{aligned} & \text { Energy }=i^{2} R t \\ & E=\left(\frac{3 V}{R}\right)^{2} R t \\ & E=\frac{9 v^{2}}{R} t . \\ & Q=\frac{9 v^{2}}{R} x t . \quad Q=m c \Delta T \\ & \therefore m c \Delta T=\frac{9 v^{2}}{R} t \quad-(1) \end{aligned}

let R^{\prime} be resistance of second wire.

$$ \begin{aligned} & R=\frac{\rho L}{A} \Rightarrow R^{\prime}= \\ & R=\frac{\rho \times 2}{A} \Rightarrow R^{\prime}=\frac{\rho \times 4}{A}=2 R \\ & \varepsilon=\frac{(N V)^{2}}{2 R} \times t \quad \text { So- } R^{\prime}=m^{\prime} c \Delta T=2 m c \Delta T \\ & 2 m c \Delta T=\frac{N^{2} V^{2}}{2 R} \times t \quad \text {-(2) } \end{aligned}

divide 1 by 2

=6

 

Posted by

rishi.raj

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