The current in the wire varies with time according to the relation i=

1.	The current in the wire varies with time according to the relation i= 4+ 2t^2 How many coulomb of charge pass a cross section of wire in time interval t= 5 s to t=10 s?
Answer» GIVEN : The current in the WIRE varies with time according to the ration $\tt{I=4+2t^2}$ . To Find : Amount of CHARGE passing through area of cross SECTION in time interval t = 5s to t = 10s. Solution : ❒ Electric current is DEFINED as the rate of charge flow per unit time in the conductor. Mathematically, I = q / t If t → 0 then I = dq / dt It is a scalar quantity having only magnitude. SI unit : A $\sf:\implies\:I=\dfrac{dq}{dt}$ $\sf:\implies\:dq=I\:dt$ Integrating both sides, we get $\displaystyle\sf:\implies\:\int dq=\int I\:dt$ $\displaystyle\sf:\implies\:\int dq=\int(4+2t^2)\:dt$ $\displaystyle\sf:\implies\:q=\bigg[4t+\dfrac{2t^3}{3}\bigg]_5^{10}$ $\sf:\implies\:q=4(10-5)+\dfrac{2(10^3-5^3)}{3}$ $\sf:\implies\:q=4(5)+\dfrac{2(1000-125)}{3}$ $\sf:\implies\:q=20+\dfrac{2(875)}{3}$ $\sf:\implies\:q=20+\dfrac{1750}{3}$ $\sf:\implies\:q=20+583.33$ $:\implies\:\underline{\boxed{\bf{\gray{q=603.33\:C}}}}$