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Q.

The quantity of charge $q$ (in coulombs) that has passed through a surface area $2 c m^{2}$ varies with time according to the equation $q = 4 t^{3} + 5 t + 6$ where t is in seconds. What is the instantaneous current through the surface at $t = 1 s$ ?

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a

$17 A$

b

$29 A$

c

$34 A$

d

$15 A$

answer is B.

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Detailed Solution

$q = 4 t^{3} + 5 t + 6 I (1 s) = {\frac{dq}{dt}}_{t = 1 s} = {(12 t^{2} + 5)}_{t = 1 s} = 17 A$

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The quantity of charge q (in coulombs) that has passed through a surface area 2cm2 varies with time according to the equation q=4t3+5t+6 where t is in seconds. What is the instantaneous current through the surface at t=1s?