Question

Given the following current equation, how much charge is displaced in the first 5 seconds?

i(t)={−t10+1 A for 0 0for t>10 s

Answer 1

The charge of 120 C will displaced in the first 5 seconds.

Explanation:

Given that,

The current equation is given by :

$i(t)=(-10t+1)\ A$

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 :

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

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

$q=\int\limits^5_0 {(-10t+1){\cdot} dt}$

$q = |-5 t^2 + t|_0^5$

$q = -5 (5)^2 + 5$

q = -120 C

So, the charge of 120 C will displaced in the first 5 seconds.

Learn more,

Electric current

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Answer 2

Answer:

3,75C

Explanation:

You neeede to integration -t/10 + 1. Thats the role:

Int(x^n.dx) = x^(n+1)  /  n+1

For this example we have:

-(t^2  / 10*2) + 1*t

-(t^2  / 20) + t

subs t for 5 we have

-(5^2  / 20) + 5

-25/20 + 5

-1,25 + 5

3,75Culombs