## Saturday, January 28, 2017

### 7.1 Solving Complex Circuits

You've all been waiting for Module 7 of the Navy Basic Electricity and Electronics series, especially since we finished Module 6 back in 2016. Module 7 is Combination Circuits and Voltage Dividers. The first section is "Solving Complex Circuits."

1. Complex circuits are circuits that are not entirely series or parallel, but some combination of the two. So they can also be called "combination" circuits or "series-parallel" circuits. First we review the rules for each kind of circuit.

Rules for Series Circuits
• Current is the same throughout the circuit.
• Voltage is additive (Kirchhoff's voltage law)--add up the voltage across each element to get the total.
• Resistance is additive--add up the individual resistances to find the total.
• Power is additive--add up the power used by each element to find the total
Rules for Parallel Circuits
• Voltage is the same in every branch of the circuit.
• Current is additive (Kirchhoff's current law)--add up the currents in each branch to get the total.
• Total resistance is more complicated. The total resistance is always less than the smallest resistance. If the branches have equal resistances, the total will be a single resistance divided by the number of branches. If there only two branches, you can multiply the two resistances and divide by their sum. For all situations, you can add up the reciprocals of each branch resistance and then take the reciprocal of that.
• Power is additive--add up the power in each branch to find the total.
2. You can guess that combination circuits simply play out the rules above in predictable ways. So, each branch of the overall circuit is its own little series circuit of sorts. Meanwhile, you could reduce all the branches of the circuit to what an equivalent, single element would look like in its place and suddenly you have an overall series circuit.

So you can redraw complex circuits in ways that reduce them to what equivalent, simple circuits might look like.