The current in a wire varies with time according to the relationship; $I = (2 + 2 t) A$, where t is time in seconds. The charge passing through a cross-section of the wire in the time interval between t = 0 s to t = 4 s is

24 C

The correct answer is Option (1) → 24 C

Given current: $I = (2 + 2t)\ \text{A}$

Charge is given by: $Q = \int I\,dt$

$Q = \int_{0}^{4} (2 + 2t)\,dt$

$Q = [2t + t^{2}]_{0}^{4}$

$Q = (2(4) + 4^{2}) - (0)$

$Q = 8 + 16 = 24\ \text{C}$

∴ Charge passing through the wire = $24\ \text{C}$