# Combination Circuits

## A combination circuit can be broken up into similar parts that are either series or parallel.

#### Key Points

• More complex connections of resistors are sometimes just combinations of series and parallel.

• Various parts of a combination circuit can be identified as series or parallel, reduced to their equivalents, and then further reduced until a single resistance is left.

• Resistance in wires reduces the current and power delivered to a resistor. If the resistance in wires is relatively large, as in a worn (or a very long) extension cord, then this loss can be significant and affect power output into appliances.

#### Terms

• A number of things that follow on one after the other or are connected one after the other.

• An arrangement of electrical components such that a current flows along two or more paths.

• An electrical circuit containing multiple resistors that are connected in a combination of both series and parallel connections.

#### Figures

1. ##### Resistor Network

In this combination circuit, the circuit can be broken up into a series component and a parallel component.

2. ##### Reducing a combination circuit

This combination of seven resistors has both series and parallel parts. Each is identified and reduced to an equivalent resistance, and these are further reduced until a single equivalent resistance is reached.

3. ##### Combination Circuits

Two parallel resistors in series with one resistor.

More complex connections of resistors are sometimes just combinations of series and parallel. This is commonly encountered, especially when wire resistances is considered. In that case, wire resistance is in series with other resistances that are in parallel.

A combination circuit Figure 3 can be broken up into similar parts that are either series or parallel, as diagramed in Figure 1. In the figure, the total resistance can be calculated by relating the three resistors to each other as in series or in parallel. R1 and R2 are connected in parallel in relation to each other, so we know that for that subset, the inverse of resistance would be equal to $\frac{1}{R_1}+\frac{1}{R_2}$ or $\frac{R_1R_2}{R_1+R_2}$ . R3 is connected in series to both R1 and R2, so the resistance would be calculated as $\frac{R_1R_2}{R_1+R_2}$ + R3. Combining these, we get:

$R = \frac{R_1R_2}{R_1+R_2}+R_3$

For more complicated combination circuits, various parts can be identified as series or parallel, reduced to their equivalents, and then further reduced until a single resistance is left, as shown in Figure 2. In this figure, the combination of seven resistors was identified by being either in series or in parallel. In the initial image, the two circled sections show resistors that are in parallel.

Reducing those parallel resistors into a single R value allows us to visualize the circuit in a more simplified manner. In the top right image, we can see that the circled portion contains two resistors in series. We can further reduce that to another R value by adding them. The next step shows that the circled two resistors are in parallel. Reducing those highlights that the last two are in series, and thus can be reduced to a single resistance value for the entire circuit.

One practical implication of a combination circuit is that resistance in wires reduces the current and power delivered to a resistor. If wire resistance is relatively large, as in a worn (or a very long) extension cord, then this loss can be significant. If a large current is drawn, the IR drop in the wires can also be significant.

#### Key Term Glossary

circuit
A pathway of electric current composed of individual electronic components, such as resistors, transistors, capacitors, inductors and diodes, connected by conductive wires or traces through which electric current can flow. T
##### Appears in these related concepts:
combination circuit
An electrical circuit containing multiple resistors that are connected in a combination of both series and parallel connections.
##### Appears in this related concept:
current
The time rate of flow of electric charge.
##### Appears in these related concepts:
inverse
Opposite in effect or nature or order.
##### Appears in these related concepts:
parallel
An arrangement of electrical components such that a current flows along two or more paths.
##### Appears in these related concepts:
power
A measure of the rate of doing work or transferring energy.
##### Appears in these related concepts:
resistance
The opposition to the passage of an electric current through that element.
##### Appears in these related concepts:
resistor
An electric component that transmits current in direct proportion to the voltage across it.
##### Appears in these related concepts:
series
A number of things that follow on one after the other or are connected one after the other.