Question

The current in a wire varies with time according to the relation i=(3.0A)+(2.0A//s)t a. How many coulomns of charge pass a cross section of the wire in the time internal between t=0 and t=4.0s? b. What constant current would transport the same charge in the same time interval?

Answer 1

Answer:

Explanation:

The rate of flow of charge is current so from the definition we solve it as follows

Answer 2

Given :

    i=(3.0A)+(2.0A/s)t

    t₁=0s

    t₂=4s

To find :

a)Charge that passes through the cross-section of while the time interval between  t=0 and t=4.0s

b)The current that will transport the same charge in same time interval

Solution:

• a)   i = (dq/dt)

      idt = dq

      $\int\limits^q_0{} \, dq$   =   $\int\limits^4_0{i} \, dt$

      $\int\limits^q_0{} \, dq$ =  $\int\limits^4_0{3+2t} \, dt$

      q=12 + 16

      q=28C

      Charge required is 28C

• b)  I = (q/t)

       = 28/4 = 7C

       Current required is 7A