Solving Current in a Circuit: How Many Equations?

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Discussion Overview

The discussion revolves around analyzing a circuit to determine the number of equations needed to solve for currents in different configurations. Participants explore the implications of defining current directions and the impact on the number of loop equations required for analysis, focusing on both DC and AC sources.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether defining current inside the loop rather than outside affects the number of equations needed to solve for the second current in the circuit.
  • Another participant asserts that regardless of the current's direction, only three loop equations are necessary to analyze the circuit.
  • A different participant suggests that if the focus is solely on the current in the rightmost resistor, the impedances of the resistor and coil can be combined, potentially reducing the number of loops to two.
  • There is a query regarding whether the voltage source is DC or AC, which could influence the type of analysis being performed (transient vs. steady-state).
  • Clarification is provided on the definitions of currents I1 and I2 in relation to the circuit's layout.
  • Another participant notes the need to write a Kirchhoff's Voltage Law (KVL) equation for each loop, mentioning the complexity introduced by a controlled voltage source in one of the loops.

Areas of Agreement / Disagreement

Participants express differing views on the number of equations required for the circuit analysis, with some asserting three equations are sufficient while others suggest that combining components could further reduce this number. The discussion remains unresolved regarding the optimal approach to defining currents and the implications for the analysis.

Contextual Notes

Participants have not reached a consensus on the number of equations needed, and there are assumptions about the nature of the voltage source that remain unaddressed. The discussion includes various interpretations of circuit components and configurations.

magnifik
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I have a circuit I need to analyze shown in the figure immediately following:
24cz9dd.png


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)?
35ddmon.png


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.
 
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magnifik said:
I have a circuit I need to analyze shown in the figure immediately following:
24cz9dd.png


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)?
35ddmon.png


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.
 
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)?
 
gneill said:
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
 
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
 
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.
 

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