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Homework Statement
An inductance of 3 mH has the following voltage waveform: for [tex]0<t<2\text{ }ms[/tex], [tex]v=15\text{ }V[/tex]; for [tex]2ms<t<4ms[/tex], [tex]v=0[/tex]; and for [tex]4\text{ }ms<t<6\text{ }ms[/tex], [tex]v=-30\text{ }V[/tex]. Assuming [tex]i(0)=0[/tex], find the current at time (a) 1 ms, (b) 4 ms, (c) 5 ms.
Ans. (a) 5 A; (b) 10 A; (c) 0
Homework Equations
[tex]u(t)=L\frac{di(t)}{dt} \Rightarrow i(t)=\frac{1}{L}\int v(t)dt[/tex]
The Attempt at a Solution
Even for (a) case (for which I somehow get the "correct" solution ), I'm not sure about the physical background: how do I use integral in [tex]i(t)[/tex] equation if I have to find currents at particular instances for t = {1, 4 and 5}?!
[PLAIN]http://img848.imageshack.us/img848/9894/dsc00990k.jpg
(a) [tex]i(t=1)=\frac{15}{L}\int dt=5t=5\text{ }A[/tex]
(b) What is [tex]v(t=4)[/tex] ... 0 V or -30 V?
(c) As in (a) case, [tex]i(t=5)=\frac{-30}{L}\int dt=-10t=-50\text{ }A \neq 0\text{ }A[/tex]
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