Question

Find current at t = 3 ms.

q = 0.4( 1-e^-250t) mC for t >= 0.

(The problem I am facing with this question is that I do not know how to solve exponential term when putting the value of t after differentiation)

Answer 1

Given:-

$\text{expression of charge, q}=0.4\left(1-e^{-250t}\right)\\\\\text{time, t}=3ms=3\times10^{-3}s$

To Find:-

current at time t=3 ms

Explanation:-

We know that current is defined as the rate of change of charge(q).

$\Rightarrow I=\dfrac{dq}{dt}=0.4\left[0-\left(e^{-250t}\times(-250)\right)\right]=100\times e^{-250t}\\\\\text{At time, }t=3\times10^{-3}s\\\\\Rightarrow I=100\times e^{-250\times3\times10^{-3}}=47.2mA=47.2\times10^{-3}A\\\\\text{Therefore, current at time t=3ms}=0.0472A$