Solving Current in a Circuit: How Many Equations?

[magnifik]

I have a circuit I need to analyze shown in the figure immediately following:

What I want to know is, if I put the current inside the loop rather than outside (as in the picture below), would I get the same answer when trying to solve for the second current (indicated by the arrow on the rightmost resistor)?

When analyzing with the current on the outside of the loop, I need 4 loop equations, correct?...
because I have the outer loop, the right loop, the left loop, and the loop on the inside of the box with the inductor and resistor.

But when analyzing with the current inside the loop, I only have 3 equations.

I am not asking for help with solving, just in understanding.

 

[jegues]

I have a circuit I need to analyze shown in the figure immediately following:

What I want to know is, if I put the current inside the loop rather than outside (as in the picture below), would I get the same answer when trying to solve for the second current (indicated by the arrow on the rightmost resistor)?

When analyzing with the current on the outside of the loop, I need 4 loop equations, correct?...
because I have the outer loop, the right loop, the left loop, and the loop on the inside of the box with the inductor and resistor.

But when analyzing with the current inside the loop, I only have 3 equations.

I am not asking for help with solving, just in understanding.

The current I1 in both images is exactly the same, it is simply passing through that one resistor. (So yes, the 2nd current you've indicated on the drawing should be the same)

You should only have 3 loop equations either way.

 

[gneill]

Following up on what jegues stated, if you're just looking for the current in the rightmost resistor, you can combine the impedances of the resistor/coil combination into a single (complex) value and you're left with two loops instead of three.

I suppose I should have asked, is the voltage source a DC source or an AC source? (Are you performing a transient analysis or a steady-state AC analysis)?

 

[magnifik]

Following up on what jegues stated, if you're just looking for the current in the rightmost resistor, you can combine the impedances of the resistor/coil combination into a single (complex) value and you're left with two loops instead of three.

I suppose I should have asked, is the voltage source a DC source or an AC source? (Are you performing a transient analysis or a steady-state AC analysis)?

steady state analysis

 

[magnifik]

I₁ would be the current going through the entire loop of the left-hand side of the circuit, right? And I₂ is the current going through the right side of the circuit

 

[gneill]

See the attached figure. I've indicated two loop currents. Note that I've assumed that the parallel RL combo in the first loop is taken as a single component.

It looks like you'll have to write a KVL equation for each loop. The controlled voltage source (k*I1) in loop 2 makes it interesting.