jangyasinniTeacher

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To find the current when the charge, (q(t)), is a function of time, we use the relationship between current and charge. The current, (I), is the rate of change of charge with respect to time, which can be mathematically expressed as:

[I(t) = frac{d}{dt}q(t)]

Given (q(t) = 3t + t^2), we need to differentiate (q(t)) with respect to (t) to find (I(t)).

Differentiating (q(t)) with respect to (t), we get:

[I(t) = frac{d}{dt}(3t + t^2) = 3 + 2t]

To find the current at (t = 2) seconds, we substitute (t = 2) into the expression for (I(t)):

[I(2) = 3 + 2(2) = 3 + 4 = 7]

Therefore, the current at 2 seconds is (7) amperes.

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Explanation: The current is defined as the rate of change of charge in a circuit ie, I =

dq/dt. On differentiating the charge with respect to time, we get 3 + 2t. At time t = 2s, I =

7A