The current in a 50 mH inductor is known to be i=120 mA, t≤0; i=A1e−500t+A2e−2000tA,t≥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 &gt; 0. b) Find the time, greater than zero, when the power at the terminals of the inductor is zero.

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The current in a 50 mH inductor is known to be  i=120 mA, t≤0; i=A1e−500t+A2e−2000tA,t≥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 &amp;gt; 0. b) Find the time, greater than zero, when the power at the terminals of the inductor is zero.

godsrvnt0706 · Accepted Answer

b)&amp;nbsp;p=vi&amp;nbsp;so we search for when the voltage of the current are zero:&amp;nbsp;i(t)=0.2e−500t−0.08e−2000t&amp;nbsp;i(t)=0⇒&amp;nbsp;0.2e−500t=008e−2000t&amp;nbsp;0.20.08=e−2000te−500t&amp;nbsp;ln⁡(2.5)=ln⁡(e−1500t&amp;nbsp;&amp;nbsp;t=−ln⁡(2.5)1500&amp;nbsp;t=−6.1⋅10−4&amp;nbsp;s&amp;nbsp;Which is not greater than zero. Lets

RizerMix · Accepted Answer

a) We know that i(0)=120 mA so we can write i(0)=A1e0+A2e0=A1+A2=0.12 A We also kno that v(0)=3 V so we write didt=−500A1e−500t−2000A2e−2000tv=Ldidt=−25A1e−500t−100A2e−2000tv(0)=−25A1e0−100A2e0=−25A1−100A2=3 Vv(0)=25A1e0−100A2e0=−25A1−100A2=3 V Now we have two equations with two unknowns: A1+A2=0.12−25A1−100A2=3 We solve this and get A1=0.2 and A2=−0.08 Now we can write the expression for the voltage v(t)=−25(0.2)e−500t−100(−0.08)e−2000tv(t)=−5e−500t+8e−2000t V

alenahelenash · Accepted Answer

You help me, thanks!

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

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