## Complex Circuits

Complex circuits have components that are in **series** and some that are in **parallel**. Lets start by reviewing series and parallel circuits and then see how a complex circuit works as a combination.

### Series Circuits and Rules (Click Here to Go to the Lesson)

A series circuit **you have no branches**, current has only one path to follow. The same current remains together through all components from the positive terminal and back to the negative of the battery.

**Ohm's Law** **(V=IR):**

You can use this at a single location (T, 1, 2, 3, and any more) as seen below

**(V**_{T}) = (I_{T})(R_{T})**(V**_{1}) = (I_{1})(R_{1})**(V**_{2}) = (I_{2})(R_{2})**(V**_{3}) = (I_{3})(R_{3})

**Overall Series Circuit Rules**

**V**_{T}= V_{1}+ V_{2}+ V_{3}+ …**I**_{T}= I_{1}= I_{2}= I_{3}= …**R**_{T}= R_{1}+ R_{2}+ R_{3}+ …

### Parallel Circuit Rules (Click Here to Go to That Lesson)

In a **parallel circuit you have branches**, multiple paths to follow. So current splits up but later comes back together as it returns to the battery.

You can use **Ohm's Law** **(V=IR)** at a single location the same as above in series circuits.

**Overall Parallel Circuit Rules**

**V**_{T}= V_{1}= V_{2}= V_{3}= …**I**_{T}= I_{1}+ I_{2}+ I_{3}+ …**1/R**_{T}= 1/R_{1}+ 1/R_{2}+ 1/R_{3 }+ ...

### Complex Circuit

Follow the current from the positive terminal of the battery in the animation. Some parts of the circuit are in series and some in parallel.

- The battery and resistor 1
_{ }are in**series:**2A of current starts at the batter and flows through both. - The branch with resistor 2, the branch with Resistor 3
_{ }and 4, and the branch with Resistor 5_{ }are in**parallel**: Current splits between these branches. - The resistor 3
_{ }and resistor 4 are in**series**: Once current goes down the branch that same current must flow from both resistors.

### Solving A Complex Circuit For Resistance

When solving for the resistance in a series circuit, the goal is to break down all the different parts making act like one single series circuit. Follow the steps or our example as we do this.

### Example Problems

**1. Solve for the total resistance of the complex circuit below.**

**2. Solve for the unknown components of the following complex circuit.**

**3. Solve for the unknown components of the following complex circuit.**

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