Question

The current passing through a terminal is given by i=4t3−3t2 A. How much charge entered the terminal between t=1 s and t=3 s.

Answer 1

The charge of 54 C will displaced in the between t=1 s and t=3 s

Explanation:

Given that,

The current equation is given by :

$i=4t^3-3t^2$

To find,

The charge is displaced in the first 5 seconds.

Solution,

The rate of change of electric charge is called electric current flowing through the circuit. It is given by :

$I=\dfrac{dq}{dt}$

$q=\int\limits {I{\cdot} dt}$

$q=\int\limits^3_1 {(4t^3-3t^2){\cdot} dt}$

$q =t^4- t^3|_1^3$

$q=[(3)^4-3^3-(1^4-1^3)]$

q = 54 C

So, the charge of 54 C will displaced in the between t=1 s and t=3 s.

Learn more,

Electric current

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