Calculation of resistor networks: A guide

Resistor networks are a central element in electrical engineering and electronics. They consist of several resistors that are connected to each other in different configurations. Calculating the total resistance of such networks is essential in order to understand the behavior of circuits - whether for analyzing the current flow or the voltage distribution. In this article, we explain the basics of series and parallel circuits, show how to break down complex circuits into smaller parts and provide practical examples to illustrate this.

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What are resistor networks?

A resistor network is a circuit consisting of several resistors connected in series, in parallel or in a combination of both arrangements. The aim is to determine the total resistance between two points. This is important not only for theoretical analysis, but also for practical applications such as the design of electronic devices or troubleshooting circuits.

Series connection of resistors

In a series circuit, the resistors are connected in series. The same current flows through each resistor, while the total voltage is distributed among the individual resistors.

Calculation of the total resistance in series

The total resistance of a series circuit is the sum of the individual resistances :

Example

Let's take three resistors with the values 10 Ω, 20 Ω and 30 Ω, which are connected in series. The total resistance is

This shows how simple the calculation is in a series connection - it is a pure addition.

Parallel connection of resistors

In a parallel circuit, the resistors are connected in such a way that they have the same voltage drop. The total current is divided between the individual branches, with each resistor receiving its own share of the current.

Calculation of the total resistance in parallel

The total resistance of a parallel circuit is calculated by the sum of the reciprocal values of the individual resistors:

For two resistors, the formula can be simplified to

Example

Let's consider two resistors with 10 Ω and 20 Ω in parallel connection. The total resistance is:

The total resistance here is smaller than the smallest individual resistance, which is a typical feature of parallel circuits.

Combined circuits: Series and parallel circuit

In real circuits, we often encounter combined networks that contain both series and parallel circuits. To calculate the total resistance, we break the circuit down into smaller, more manageable parts.

Method for breaking down complex circuits

1st Identification: Find groups of resistors connected directly in series or in parallel. 2 Simplification: Calculate the equivalent resistance for these groups. 3 Iteration: Replace the simplified parts with their equivalent resistor and repeat the process until only a single resistor remains.

Example of a combined circuit

Let's imagine a circuit in which two resistors and are connected in parallel and this parallel duo is in series with a third resistor .

1st Calculation of the parallel duo:

2nd Addition of the series resistance:

This example shows how to proceed step by step to solve a combined circuit.

Summary

The calculation of resistor networks is an indispensable skill in electrical engineering. With an understanding of series circuits (addition of resistances) and parallel circuits (sum of reciprocals) and the ability to break down complex circuits into smaller parts, you can accurately determine the total resistance. This knowledge can be applied in many areas - from simple household appliances to complex industrial systems. Use this guide as a foundation to develop your skills and solve practical problems in electrical engineering.