Question

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

Answer 1

d)50.4 C

Step-by-step explanation:

We are given that

`I(t)=6A+(4.8 A/s)t`

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

`dq=Idt`

Integrating on both sides

`q=\int_(0)_(3.5) (6+4.8 t)dt`

`q=[6t+2.4t^2]^(3.5)_(0)`

`q=6(3.5)+2.4(3.5)^2=50.4 C`

Hence, option d is true.