The current in a wire varies with time according
to the relation,
i = (3A) + (2 A/s)t
() How many coulombs of charge pass through a cross-section
of the wire in the time interval between t = 0 and t = 4 s?
(i) What constant current would transport the same charge in
the same time interval?
Answers
Given:
The current in a wire varies with time according to the relation, i = (3A) + (2 A/s)t
To find:
(i) How many coulombs of charge pass through a cross-section of the wire in the time interval between t = 0 and t = 4 s?
(ii) What constant current would transport the same charge in the same time interval?
Solution:
From given, we have,
The current in a wire varies with time according to the relation, i = (3A) + (2 A/s)t
I = 3 + 2t
we use the formula,
I = dq/dt
⇒ dq = I dt
integrating on both the sides, we get,
∫ dq = ∫ I dt
∫ dq = ∫ (3 + 2t) dt
q = ∫ 3 dt + ∫ 2t dt
q = 3t + 2(t²/2)
∴ q = 3t + t²
time interval between t = 0 and t = 4 s
[3t + t²]_4 - [3t + t²]_0
= {[3(4) + 4²] - [3(0) + 0²]}
= {12 + 16 - 0}
= 28
(i) 28 coulombs of charge pass through a cross-section of the wire in the time interval between t = 0 and t = 4 s.
Constant current is given by the formula,
Constant current = q/t
= 28 C/ 4 s
= 7 C/S
(ii) 7 A of constant current would transport the same charge in the same time interval.