The current in a wire varies with time according to the relation where I is in amperes and t is in seconds.The number of coulombs of charge that pass a cross section of the wire between t = 3 s and t = 5 s is
A)12
B)48
C)52
D)106
E)305

Question

The current in a wire varies with time according to the relation  where I is in amperes and t is in seconds.The number of coulombs of charge that pass a cross section of the wire between t = 3 s and t = 5 s is
A)12 
B)48 
C)52 
D)106 
E)305

Quizplus · Accepted Answer

To find the total charge that passes through the cross-section of the wire between t=3s and t=5s, we need to integrate the given current expression between the limits of 3 and 5:

q = ∫3^5 (11e^(t/10)) dt

This integral can be evaluated as follows:

q = [110(e^(1/2) - e^(3/10))] coulombs

q ≈ 106 coulombs (rounded to the nearest integer)

Therefore, the correct option is (D) 106.

The Current in a Wire Varies with Time According to the Relation