# How to analyze a complex circuit

## Homework Equations

Kirchoff's Current and Voltage laws

## The Attempt at a Solution

How do you go about analyzing a complex circuit like this? Do you just write out the current equation for each highlighted junction and voltage equations for each loop? Is there a quick way to determine which things are in parallel or in series with one another?

## Answers and Replies

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Hesch
Gold Member
How do you go about analyzing a complex circuit like this?
It can be done in different ways. I will suggest:

Make 3 KCL equations as for B, C, D and determine the voltages VB, VC, VD.

Example for the node, C:

IBC - IC0 - ICD = 0 →

( VB -VC )/R2 - ( VC - 0 )/R5 - ( VC - VD )/R4 = 0

Now, make two more equations as for the nodes B, D and solve the three voltages.

Currents are calculated simply by Ohm's law.

cnh1995
Homework Helper
Gold Member
What is the question here? What is asked?

gneill
Mentor
How do you go about analyzing a complex circuit like this? Do you just write out the current equation for each highlighted junction and voltage equations for each loop? Is there a quick way to determine which things are in parallel or in series with one another?
There are several possible approaches, but they have similar complexity. Basic KVL and KCL will do it, or their slightly more polished versions: mesh and nodal analysis. The given circuit doesn't have any series or parallel resistor simplification opportunities, nor are the component values chosen in such a way that there are symmetries to exploit to simplify the analysis.

The circuit has three independent loops (or "meshes") and three essential nodes (look up the terms if you're not familiar with them). That means any way you slice it you need to solve three equations in three unknowns.

Re component connections: Series connections are easy to spot, there being two components connected, all alone, at a common junction. Spotting parallel components can be trickier, but it becomes second nature with practice. Until you get sufficient practice though, a sure way to find them is to color each node in the circuit with a different color (so keep a few different highlighters or markers around). Any components with connections to the same pair of nodes (colors) are in parallel. Just list the color connection pairs for each component and match them up.

Was there anything else you needed to know about the circuit?

Last edited:
Thank you everyone for your help. I think I understand it now, but I just need more practice.