Current Electricity Ques 59
- 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 is now connected in series with a wire of the same material and cross-section but of length $2$ $L$. The temperature of the wire is raised by the same amount $\Delta T$ in the same time. The value of $N$ is
$(2001,2 M)$
(a) $4$
(b) $6$
(c) $8$
(d) $9$
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Answer:
Correct Answer: 59.( b )
Solution:
Formula:
- In the first case $\frac{(3 E)^{2}}{R} t=m s \Delta T$ $\quad$ …….(i)
$ [H=\frac{V^{2}}{R} t] $
When length of the wire is doubled, resistance and mass both are doubled.
Therefore, in the second case,
$ \frac{(N E)^{2}}{2 R} \cdot t=(2 m) s \Delta T $ $\quad$ …….(ii)
Dividing Eq. (ii) by (i), we get
$ \frac{N^{2}}{18}=2 \text { or } N^{2}=36 \text { or } N=6 $
BETA
