Solving Current in a Circuit: How Many Equations?

In summary, the conversation discusses a circuit that needs to be analyzed, with a question about whether putting the current inside the loop rather than outside would affect the solution for a specific current. It is noted that with the current outside the loop, four loop equations are needed, but with the current inside the loop, only three are needed. It is also suggested to combine the impedances of the resistor/coil combination into a single complex value to reduce the number of loops. The type of voltage source and analysis being performed is clarified. Ultimately, it is concluded that two loop equations are needed and the conversation ends with a brief discussion of the loop currents in the circuit.
  • #1
magnifik
360
0
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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  • #2
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.
 
  • #3
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)?
 
  • #4
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
 
  • #5
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
 
  • #6
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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FAQ: Solving Current in a Circuit: How Many Equations?

What is the purpose of solving current in a circuit?

Solving current in a circuit allows us to understand how electricity flows through a circuit and how different components affect the flow of current. This information is crucial in designing and troubleshooting circuits.

How many equations are needed to solve for current in a circuit?

The number of equations needed depends on the complexity of the circuit. In a simple series or parallel circuit, only one equation is needed, while in a more complex circuit with multiple branches, multiple equations may be required.

What are the basic equations used to solve for current in a circuit?

The two basic equations used to solve for current in a circuit are Ohm's Law (I = V/R) and Kirchhoff's Current Law (the sum of the current entering a node is equal to the sum of the current leaving the node).

Can current be solved for in a circuit with only one unknown variable?

Yes, as long as the circuit is a simple series or parallel circuit, the current can be solved for with only one unknown variable. However, in more complex circuits, multiple unknown variables may be present and more equations will be needed to solve for current.

What are some common mistakes to avoid when solving for current in a circuit?

Some common mistakes to avoid include not taking into account the direction of current flow, not properly labeling the values in the circuit, and not considering all the components and their effects on current flow. It is important to carefully analyze the circuit and use the correct equations and values in order to accurately solve for current.

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