Charge passing through a conductor of cross-section area A = 0.3 $m^{2}$ is given by $q = 3 t^{2} + 5 t + 2$ in coulomb, where t is in second. What is the value of drift velocity at t = 2s?
(Given, n = 2 x $10^{25} / m^{3}$ )

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1.77 x $10^{- 5} m / s$

0.77 x $10^{- 5} m / s$

0.57 x $10^{- 5} m / s$

2.08 x $10^{- 5} m / s$

answer is B.

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Detailed Solution

$drift velocity related with current as$

$i = {neAv}_{d}$

$\frac{d q}{d t} = n e A v_{d}$

$q = 3 t^{2} + 5 t + 2$

$\frac{d q}{d t} = 6 t + 5$

$a t t = 2 \frac{d q}{d t} = i = 17$

$v_{d} = \frac{i}{n e A} = \frac{17}{2 \times 10^{25} \times 1.6 \times 10^{- 19} \times 0.3} = 17.7 \times 10^{- 6}$

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