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

diferira7c 2022-01-17 Answered
The current in a 50 mH inductor is known to be
i=120 mA, t0; i=A1e500t+A2e2000tA,t0
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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Answers (3)

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(t)=0.2e500t0.08e2000t
i(t)=0
0.2e500t=008e2000t
0.20.08=e2000te500t
ln(2.5)=ln(e1500t
t=ln(2.5)1500
t=6.1104 s
PSKWhich is not greater than zero. Lets
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RizerMix
Answered 2022-01-19 Author has 438 answers

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=500A1e500t2000A2e2000tv=Ldidt=25A1e500t100A2e2000tv(0)=25A1e0100A2e0=25A1100A2=3 Vv(0)=25A1e0100A2e0=25A1100A2=3 V
Now we have two equations with two unknowns:
A1+A2=0.1225A1100A2=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)e500t100(0.08)e2000tv(t)=5e500t+8e2000t V

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alenahelenash
Answered 2022-01-23 Author has 343 answers

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