Current Electricity 3 Question 11
10. 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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Solution:
- In the first case $\frac{(3 E)^{2}}{R} t=m s \Delta T$
$$ H=\frac{V^{2}}{R} t $$
When length of the wire is doubled, resistance and mass both are doubled.
Therefore, in the second case,
$$ \frac{(N E)^{2}}{2 R} \cdot t=(2 m) s \Delta T $$
Dividing Eq. (ii) by (i), we get
$$ \frac{N^{2}}{18}=2 \text { or } N^{2}=36 \text { or } N=6 $$
