A source of e.m.f. E = 15 ,V and having negligible internal resis… - Vidyadip

MCQ

A source of $e.m.f.$ $E = 15\,V$ and having negligible internal resistance is connected to a variable resistance so that the current in the circuit increases with time as $i = 1.2 t + 3$. Then, the total charge that will flow in first five second will be ............... $C$

A
$10$
B
$20 $
✓
$30$
D
$40$

✓

Answer

Correct option: C.

$30$

c
$i = \frac{{dQ}}{{dt}}$ $ \Rightarrow $ $dQ = idt$ $ \Rightarrow $ $Q = \int_{\,{t_1}}^{\,{t_2}} i \,dt = \int_0^5 {(1.2t + 3)\,} dt$

$ = \left[ {\frac{{1.2{t^2}}}{2} + 3t} \right]_0^5 = 30\,C$

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