A current in a wire is given by the equation, $I = 2 t^{2} - 3 t + 1$ , the charge through cross section of wire in time interval $t = 3$ s to $t = 5$ s is?

32.33

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43.34

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45.5

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42

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Solution

The correct option is B $43.34$ C
Given: $I = 2 t^{2} - 3 t + 1$
As $I = \frac{d Q}{d t}$ ;

$d Q = I d t$ ;
$d Q = (2 t^{2} - 3 t + 1) d t$
$\int d Q = \int_{t = 3}^{t = 5} (2 t^{2} - 3 t + 1) d t;$

$Q = {[\frac{2 t^{3}}{3} - \frac{3 t^{2}}{2} + t]}_{3}^{5}$
$= [\frac{2}{3} (125 - 27) - \frac{3}{2} (25 - 9) + 2] = 43.34$ C.

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A current in a wire is given by the equation, I=2t2−3t+1, the charge through cross section of wire in time interval t=3s to t=5s is?

The correct option is B 43.34CGiven:I=2t2−3t+1As I=dQdt; dQ=Idt; dQ=(2t2−3t+1)dt∫dQ=∫t=5t=3(2t2−3t+1)dt;Q=[2t33−3t22+t]53=[23(125−27)−32(25−9)+2]=43.34C.

A current in a wire is given by the equation, $I = 2 t^{2} - 3 t + 1$ , the charge through cross section of wire in time interval $t = 3$ s to $t = 5$ s is?