First slide

electric current

Question

The current in a conductor varies with time t as $I = 2 t + 3 t^{2},$ where I is in ampere and t in seconds. Electric charge flowing through a section of the conductor during t = 2 sec to t = 3 sec is

Moderate

A

10 C
B

24 C
C

33 C
D

44 C

Solution

$\begin{array}{l} dQ = Idt \Rightarrow Q = \int_{t = 2}^{t = 3} Idt = [2 \int_{2}^{3} tdt + 3 \int_{2}^{3} t^{2} dt] \\ = {[t^{2}]}_{2}^{3} + {[t^{3}]}_{2}^{3} = (9 - 4) + (27 - 8) = 5 + 19 = 24 C \end{array}$

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