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The current in a wire varies with time according to the equation I(t) = 6 A + (4.8 A/s)t, where t is in seconds. How many coulombs of charge pass a cross section of the wire in the time period between t = 0.00 s and 3.5 s.

a)102.9 C
b)21 C
c)3.5 C
d)50.4 C
e)29.4 C

Respuesta :

lublana

Answer:

d)50.4 C

Explanation:

We are given that

[tex]I(t)=6A+(4.8 A/s)t[/tex]

Where t (in s)

We have to find the charge pass a cross section of the wire in the time period t=0 s and t=3.5 s

We know that

[tex]dq=Idt[/tex]

Integrating on both sides

[tex]q=\int_{0}_{3.5} (6+4.8 t)dt[/tex]

[tex]q=[6t+2.4t^2]^{3.5}_{0}[/tex]

[tex]q=6(3.5)+2.4(3.5)^2=50.4 C[/tex]

Hence, option d is true.