Question

The quantity of charge passing through a surface of area 1.82 cm2 varies with time as q = q1 t 3 + q2 t + q3 , where q1 = 5.2 C/s 3 , q2 = 2.5 C/s, q3 = 6.5 C, and t is in seconds. What is the instantaneous current through the surface at t = 1.1 s? Answer in units of A.

Answer 1

Current through the surface at t = 1.1 s is 21.37 A.

Step-by-step explanation:

The charge is passing through a surface of area varies with time as :

`q=q_1t^3+q_2t+q_3`

Here,

`q_1=5.2\ C/s^3\\\\q_2=2.5\ C/s\\\\q_3=6.5\ C`

t is in seconds

`q=5.2t^3+2.5t+6.5`

The rate of change of electric charge is called electric current. It is given by :

`I=(dq)/(dt)\\\\I=(d(5.2t^3+2.5t+6.5))/(dt)\\\\I=15.6t^2+2.5`

At t = 1.1 s, Current,

`I=15.6(1.1)^2+2.5\\\\I=21.37\ A`

So, the instantaneous current through the surface at t = 1.1 s is 21.37 A.