The current through a wire depends on time as $\text{i}=\text{i}_0+\alpha\text{t},$
Where $\text{i}_0=10\text{A}$ and $\alpha=4\text{A/ s}.$ Find the charge that crosses through a section of the wire in 10 seconds.
Where $\text{i}_0=10\text{A}$ and $\alpha=4\text{A/ s}.$ Find the charge that crosses through a section of the wire in 10 seconds.
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$\text{i}=\text{i}_0+\alpha\text{t},\ \text{t}=10\text{sec},$ $\text{i}_0=10\text{A},\alpha=4\text{A}/\text{ sec}$
$\text{q}=\int\limits^\text{t}_0\text{idt}=\int\limits^\text{t}_0(\text{i}_0+\alpha\text{t})\text{dt}=\int\limits^\text{t}_0\text{i}_0\text{dt}+\int\limits^\text{t}_0\alpha\text{tdt}$
$=\text{i}_0\text{t}+\alpha\frac{\text{t}^2}{2}=10\times10+4\times\frac{10\times10}{2}$
$=100+200=300\text{C}.$
$\text{q}=\int\limits^\text{t}_0\text{idt}=\int\limits^\text{t}_0(\text{i}_0+\alpha\text{t})\text{dt}=\int\limits^\text{t}_0\text{i}_0\text{dt}+\int\limits^\text{t}_0\alpha\text{tdt}$
$=\text{i}_0\text{t}+\alpha\frac{\text{t}^2}{2}=10\times10+4\times\frac{10\times10}{2}$
$=100+200=300\text{C}.$
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