Current through an Inductor in an RL circuit

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maxpound18
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Homework Statement



Find i0(t) see attached picture

Homework Equations



io(t) = iinfinite + (i0- - iinfinite)e-Rt/L

The Attempt at a Solution



I first re-drew the diagram for when the switch has NOT been closed, which is esssentially the same thing without the 37.5 V Source and the adjacent 10 ohm resistor.

I then found V(phi) using ohms law since the current through both the resistors should be the same. The current is (i=V/R) which is (250/50= 5 Amps)
So, V(phi) = iR which is (5amps*10ohms = 50 V)

I then applied Kirkchoff's Current Law to the node between the inductor, the dependent source, and the 10 ohm resistor.
0 = -(250/50) + 9V(phi) + i0
0 = -5 + 9V(phi) + i0
0 = -5 + 9(50) + i0
i0 = -445 Amps (This seems wrong) but moving on...then i drew the diagram for when t > 0
 
Attachments
  • Hand-drawn circuit schematic with a 70 ohm resistor, an 8.72 mH inductor carrying current i0, a dependent voltage source of 9 V_phi, a 10 ohm resistor, a switch at t=0, a 37.5 V source, and a 250 V source.
    IMAG0233.jpg
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Last edited:
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sorry i left out a resistor.

THIS is the correct drawing
 
Attachments
  • Handwritten circuit schematic on lined paper with a 872 nH inductor carrying current i_o, a 70 ohm resistor, a dependent current source 9V_g, 10 ohm and 40 ohm resistors, a switch marked t=0, a 10 ohm resistor with a 325 V source, a 250 V source, and the label i_o(t) = ?
    IMAG0235.jpg
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For when t > 0

here are source conversions.
 
Attachments
  • Two handwritten circuit schematics on lined paper: the top has a 20 ohm resistor, 8.7 ohm and 10 ohm series resistors, a dependent current source 9V0, a 10 ohm resistor, a 3.75 A current source and a 40 ohm resistor with a 250 V source; the bottom shows the source-converted version.
    IMAG0236.jpg
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and more conversions
 
Attachments
  • Hand-drawn circuit diagram above a downward arrow, with the simplified circuit below. Top circuit: 87.2 mH inductor, 20 ohm resistor, dependent current source 9V_phi, 10 ohm resistor, 3.75 A and 6.25 A current sources, 10 ohm and 40 ohm resistors. Bottom: 87.2 mH inductor, 7 ohm resistor, 9V_phi source, 10 ohm resistor, 8 ohm resistor, 10 A source.
    IMAG0238.jpg
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My question at this point is how do I reduce THIS circuit down to one resistor with the inductor? And what am i supposed to do with the Dependent Current Source.

The values I calculated for V(phi) and i0 are 44.4V and -395.2A respectively.
 
Attachments
  • Handwritten circuit schematic on lined paper: a 67.2 mH inductor and 10 Ω resistor along the top wire, a 20 Ω resistor on the left branch, an 8 Ω resistor and 80 V source on the right, and a dependent current source labelled 9 V_φ in the middle branch, with V_φ marked across the 10 Ω resistor.
    IMAG0239.jpg
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