Question

If I = t² + 5, find the charge Q flow through a cross section between 0 to 3 sec. Also find the number of electrons that flows in this time

Answer 1

▶ Solution :

Given :

▪ $\bf\red{I=t^2+5}$

To Find :

▪ Charge flow through a cross section between 0 to 3 second.

▪ The number of electrons that flows in this time.

Formula :

✏ Formula of current in terms of charge flow and time interval is given by

$\underline{\boxed{\bf{\pink{I=\dfrac{dQ}{dt}}}}}$

Calculation :

$\displaystyle\rightarrow\sf\:dQ=I\:dt\\ \\ \rightarrow\sf\:Q=\int{dQ}=\int{I\:dt}\\ \\ \rightarrow\sf\:Q=\int(t^2+5)\:dt\\ \\ \rightarrow\sf\:Q=\lim{0\to 3}\:\:{\huge[}\dfrac{t^3}{3}+5t{\huge]}\\ \\ \rightarrow\sf\:Q=\dfrac{(3)^3}{3}+5(3)\\ \\ \rightarrow\sf\:Q=9+15\\ \\ \rightarrow\boxed{\bf{\purple{Q=24\:C}}}\\ \\ \rightarrow\bf\:Q=ne\\ \\ \rightarrow\sf\:24=n\times 1.6\times 10^{-19}\\ \\ \rightarrow\sf\:n=\dfrac{24}{1.6\times 10^{-19}}\\ \\ \rightarrow\boxed{\bf{\orange{no.of\:electrons=1.5\times 10^{20}}}}$