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.

diferira7c
2022-01-17
Answered

The current in a 50 mH inductor is known to be

$i=120\text{}mA,\text{}t\le 0;\text{}i={A}_{1}{e}^{-500t}+{A}_{2}{e}^{-2000t}A,t\ge 0$

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.

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.

You can still ask an expert for help

godsrvnt0706

Answered 2022-01-19
Author has **31** answers

b) $p=vi$ so we search for when the voltage of the current are zero:

$i\left(t\right)=0.2{e}^{-500t}-0.08{e}^{-2000t}$

$i\left(t\right)=0\Rightarrow$

$0.2{e}^{-500t}=\frac{0}{08}{e}^{-2000t}$

$\frac{0.2}{0.08}=\frac{{e}^{-2000t}}{{e}^{-500t}}$

$\mathrm{ln}\left(2.5\right)=\mathrm{ln}({e}^{-1500t}$

$t=\frac{-\mathrm{ln}\left(2.5\right)}{1500}$

$t=-6.1\cdot {10}^{-4}\text{}s$

PSKWhich is not greater than zero. Lets

PSKWhich is not greater than zero. Lets

RizerMix

Answered 2022-01-19
Author has **438** answers

a) We know that

We also kno that

Now we have two equations with two unknowns:

We solve this and get

Now we can write the expression for the voltage

alenahelenash

Answered 2022-01-23
Author has **343** answers

You help me, thanks!

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