Electrical circuits can become immensely complicated. This circuit is a polynomial plotter, which allows users to plot polynomials and evaluate functions at various values.

### Combined Series-Parallel Circuits

Most circuits are not just a series or parallel circuit; most have resistors in parallel and in series. These circuits are called **combination circuits**. When solving problems with such circuits, use this series of steps.

- For resistors connected in parallel, calculate the single equivalent resistance that can replace them.
- For resistors in series, calculate the single equivalent resistance that can replace them.
- By repeating steps 1 and 2, you can continually reduce the circuit until only a single equivalent resistor remains. Then you can determine the total circuit current. The voltage drops and currents though individual resistors can then be calculated.

**Example Problem:** In the combination circuit sketched below, find the equivalent resistance for the circuit, find the total current through the circuit, and find the current through each individual resistor.

**Solution:** We start by simplifying the parallel resistors and .

We then simplify and which are series resistors.

We can then find the total current,

All the current must pass through , so .

The voltage drop through is .

Therefore, the voltage drop through and is 11.4 volts.

and

#### Summary

- Combined circuit problems should be solved in steps.

#### Practice

Video teaching the process of simplifying a circuit that contains both series and parallel parts.

http://www.youtube.com/watch?v=In3NF8f-mzg

Follow up questions:

- In a circuit that contains both series and parallel parts, which parts of the circuit are simplified first?
- In the circuit drawn below, which resistors should be simplified first?

#### Review

- Two 60.0Ω resistors are connected in parallel and this parallel arrangement is then connected in series with a 30.0Ω resistor. The combination is placed across a 120. V potential difference.
- Draw a diagram of the circuit.
- What is the equivalent resistance of the parallel portion of the circuit?
- What is the equivalent resistance for the entire circuit?
- What is the total current in the circuit?
- What is the voltage drop across the 30.0Ω resistor?
- What is the voltage drop across the parallel portion of the circuit?
- What is the current through each resistor?

- Three 15.0 Ohm resistors are connected in parallel and the combination is then connected in series with a 10.0 Ohm resistor. The entire combination is then placed across a 45.0 V potential difference. Find the equivalent resistance for the entire circuit.