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Q.

The current in a conductor varies with time ‘t’ as I = 3t + 4t² . Where I in amp and t in sec. The electric charge flows through the section of the conductor between t = 1s and t = 3s

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a

$\frac{3}{140} C$

b

$\frac{140}{3} C$

c

$\frac{3}{14} C$

d

$\frac{14}{3} C$

answer is C.

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Detailed Solution

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$\begin{matrix} I = \frac{dq}{dt}; dq = Idt; \int dq = \int_{1}^{3} Idt = \int_{1}^{3} (3 t + 4 t^{2}) dt \\ = \frac{3 t^{2}}{2} + \frac{4 \times t^{3}}{3} = \frac{3}{2} (3)^{2} + \frac{4}{3} (3)^{3} - \frac{3}{2} (1)^{2} - \frac{4}{3} (1)^{3} \\ = \frac{140}{3} C \end{matrix}$

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The current in a conductor varies with time ‘t’ as I = 3t + 4t2 . Where I in amp and t in sec. The electric charge flows through the section of the conductor between t = 1s and t = 3s