Physics
Textbooks
Boundless Physics
Circuits and Direct Currents
Resistors in Series and Parallel
Physics Textbooks Boundless Physics Circuits and Direct Currents Resistors in Series and Parallel
Physics Textbooks Boundless Physics Circuits and Direct Currents
Physics Textbooks Boundless Physics
Physics Textbooks
Physics
Concept Version 13
Created by Boundless

Combination Circuits

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

Learning Objective

  • Describe arrangement of resistors in a combination circuit and its practical implications


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

  • series

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

  • parallel

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

  • combination circuit

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


Full Text

Combination Circuits

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 can be broken up into similar parts that are either series or parallel, as diagrammed in . 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:

Resistor Network

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

Combination Circuits

Two parallel resistors in series with one resistor.

$ \frac{1}{R_1}+ \frac{1}{R_2}$ orĀ $ \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:

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

Complex Combination Circuits

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 . 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 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.

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. Combination circuit can be transformed into a series circuit, based on an understanding of the equivalent resistance of parallel branches to a combination circuit. A series circuit can be used to determine the total resistance of the circuit. Essentially, wire resistance is a series with the resistor. It thus increases the total resistance and decreases the current. 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.

[ edit ]
Edit this content
Prev Concept
Resistors in Parallel
Charging a Battery: EMFs in Series and Parallel
Next Concept
Subjects
  • Accounting
  • Algebra
  • Art History
  • Biology
  • Business
  • Calculus
  • Chemistry
  • Communications
  • Economics
  • Finance
  • Management
  • Marketing
  • Microbiology
  • Physics
  • Physiology
  • Political Science
  • Psychology
  • Sociology
  • Statistics
  • U.S. History
  • World History
  • Writing

Except where noted, content and user contributions on this site are licensed under CC BY-SA 4.0 with attribution required.