Question

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 1

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

$\displaystyle\sf:\implies\:\int dq=\int I\:dt$

$\displaystyle\sf:\implies\:\int dq=\int(4+2t^2)\:dt$

$\displaystyle\sf:\implies\:q=\bigg[4t+\dfrac{2t^3}{3}\bigg]_5^{10}$

$\sf:\implies\:q=4(10-5)+\dfrac{2(10^3-5^3)}{3}$

$\sf:\implies\:q=4(5)+\dfrac{2(1000-125)}{3}$

$\sf:\implies\:q=20+\dfrac{2(875)}{3}$

$\sf:\implies\:q=20+\dfrac{1750}{3}$

$\sf:\implies\:q=20+583.33$

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