# The current in a 50 mH inductor is known to be i=120\

The current in a 50 mH inductor is known to be

The voltage across the inductor (passive sign convention) is 3 V at t =0. a) Find the expression for the voltage across the inductor for t > 0. b) Find the time, greater than zero, when the power at the terminals of the inductor is zero.
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godsrvnt0706
b) $p=vi$ so we search for when the voltage of the current are zero:
$i\left(t\right)=0.2{e}^{-500t}-0.08{e}^{-2000t}$
$i\left(t\right)=0⇒$
$0.2{e}^{-500t}=\frac{0}{08}{e}^{-2000t}$
$\frac{0.2}{0.08}=\frac{{e}^{-2000t}}{{e}^{-500t}}$
$\mathrm{ln}\left(2.5\right)=\mathrm{ln}\left({e}^{-1500t}$
$t=\frac{-\mathrm{ln}\left(2.5\right)}{1500}$

PSKWhich is not greater than zero. Lets
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RizerMix

a) We know that $i\left(0\right)=120$ mA so we can write

We also kno that so we write

Now we have two equations with two unknowns:
${A}_{1}+{A}_{2}=0.12\phantom{\rule{0ex}{0ex}}-25{A}_{1}-100{A}_{2}=3$
We solve this and get

Now we can write the expression for the voltage

alenahelenash