Solve Confusing Inductor Question: Finding Parts b,c,d - Help Needed

[tesla58]

Summary: Confusing Inductor question

I've been in trouble with a question for whole days , trouble is finding parts b,c and d.
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in the solving of part b WHEN we find i0(t) ,why minus is in front of integral(-1/4 coefficient one) and why +5 why not -5 ? I think it relates passive sign convention but i do not know how to determine it.

and also part c VLeq = V3.2 + V0 where does this equation come from ? Please some help and sorry for the bad english and if i open the thread to wrong place.

 

[mitochan]

Hi.

in the solving of part b WHEN we find i0(t) ,why minus is in front of integral(-1/4 coefficient one) and why +5 why not -5 ? I think it relates passive sign convention but i do not know how to determine it.

Voltage and current here do not seem to follow usual sign convention, "current flows from voltage + to voltage -". I think it is the reason why.

where does this equation come from ?

It also comes from sign convention of currents. Oposite direction of $v_{3.2}$ and $v_0$ comes from opposite direction definition between current $i_0$ and currents $i_1$ and $i_2$ .

 

[zoki85]

Hint: Determine what element is in black box, and find its value, setting t=0 in the equation v(t)=2000*e^-100t

 

[Babadag]

In my opinion the KVL circulation it has to be:
-3.2*dio/dt+vo+1*di1/dt=0 and if
di1/dt+di2/dt=-dio/dt and 1*di1/dt=4*di2/dt then
dio/dt*(3.2+0.8)=-Vo
At t=0- Vo=0 [the switch is still close].
io[0-]=5

io=-1/4∫vo|t=0+ to t=t| +5[io t=0-]

 

[tesla58]

I think I found a way. İt is about which one supply power to the circuit and which one receive. So here i1(0)=-6
in the beginning the most big current 6 amp it means that it supply power to the circuit ,according to sign convention current must be the direction of voltage increase and we also should consider that i1 acctually downward.And i0 must receive power so its current direction is direction of voltage drop.Finally we implement KVL
analysis.

 

[rude man]

1. guess a really simple component for the black box
2 .then the given v(t) is a big hint once you've found i(0)
3. Verify that your guess is correct by computing a time constant involving the inductors and the black box.

The rest is straight-forward.