NEET-XII-Physics
32: Electric Current in Conductors
- #4The current through a wire depends on time as i = i0 + αt,
where i0 = 10 A and α = 4 As-1. Find the charge that crosses through a section of the wire in 10 seconds.Ans : Current through the wire varies with time as
i = i0 + α t
Time interval, t = 10 s
i0 = 10 A
α = 4 A/sec
We know that for variable current,
`` q={\int }_{0}^{t}i\,\mathrm{\,d\,}t``
`` \Rightarrow q={\int }_{0}^{t}\left({i}_{0}+\alpha t\right)\,\mathrm{\,d\,}t``
`` \Rightarrow q={i}_{0}t+\frac{\alpha {t}^{2}}{2}``
`` \therefore q=10\times 10+4\times \frac{{\left(10\right)}^{2}}{2}``
`` =100+200``
`` =300\,\mathrm{\,C\,}``
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