UNDERSTANDING & CALCULATING COMBINATION CIRCUITS

INTRODUCTION 

A "COMBINATION CIRCUIT" is (as you may have already guessed) a circuit that is a blend of series paths and parallel paths.  See Figure for a visual explanation.   Most circuits are of this variety.  Don't be afraid to tackle these circuits as far as the math goes.  You merely have to break each part of the circuit down into either a series circuit or parallel circuit. Here's how this is done: 


BASICS

You must first figure out the resistance of each individual parallel path in the circuit.  Let's take the circuit to the right as an example.  There is an 8 Ohm resistor in series (R1) and  two 4 Ohm  resistors in parallel, R2||R3 (Note: The || means that the two resistors are in parallel). To figure out the total resistance of that section of the circuit we use the following: 

1. Find the resistance of the parallel circuit using the parallel formula.  
1/R = 1/R2 + 1/R3 
1/R = 1/4 + 1/4 
1/R = .25 + .25 
1/R = .5 
R2||R3 = 1/.5 = 2 Ohms 




Now that you know the resistance of the parallel 'subcircuit', you add all the series resistances.  Remember the total resistance of R2||R3 can now be plugged into the series calculation to figure out the remaining values using Ohm's Law. See figure to the left. 

2: Find the total resistance in the circuit by adding  R1 and R2||R3. 
Rt = R1 + (R2||R3) 
Rt = 8 Ohms  + 2 Ohms 
R total = 10 Ohms



Now that you know the total resistance of the circuit you can figure out the total amperage using Ohm's Law. 

I total = V divide by R total 
It = 10V / 10 Ohms 
I total = 1 Amp.

From here you can figure out each components voltage drop or current.
The best advice in finding the values for a combination circuit is to first break each part of the circuit down into series and parallel sections and follow those formulas. Once that is complete, combine them for your master calculations.