Question: Q. 12. (i) Deduce the relation between current $I$ flowing through a conductor and drift velocity $v_{d}$ of the electrons.
(ii) Figure shows a plot of current ’ $I$ ’ flowing through the cross-section of a wire versus the time ’ $t$ ‘. Use the plot to find the charge flowing in $10 \mathrm{~s}$ through the wire.
U] [O.D. I, II, III 2015$]$
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Solution:
Ans. (i) According to the figure,
$$ \Delta x=v_{d} \Delta t $$
Hence, amount of charge crossing area Antime $\Delta t$
(ii) Charge flowing $=\sum I \Delta t$
$$ \begin{aligned} & =\text { area under the curve } \ & =\left[\frac{1}{2} \times 5 \times 5+5(10-5)\right] \mathrm{C} \ & =37.5 \mathrm{C} \end{aligned} $$
