A linear resistor is a linear, passive two-terminal electrical component that implements electrical resistance as a circuit element. The current through a resistor is in direct proportion to the voltage across the resistor's terminals. Thus, the ratio of the voltage applied across a resistor's terminals to the intensity of current through the circuit is called resistance. This relation is represented by Ohm's law:
Resistors are common elements of electrical networks and electronic circuits and are ubiquitous in most electronic equipment. Practical resistors can be made of various compounds and films, as well as resistance wire (wire made of a high-resistivity alloy, such as nickel-chrome). Resistors are also implemented within integrated circuits, particularly analog devices, and can also be integrated into hybrid and printed circuits.
The ohm (symbol: Ω) is the SI unit of electrical resistance, named after Georg Simon Ohm. An ohm is equivalent to a volt per ampere. Since resistors are specified and manufactured over a very large range of values, the derived units of milliohm (1 mΩ = 10−3 Ω), kilohm (1 kΩ = 103 Ω), and megaohm (1 MΩ = 106 Ω) are also in common usage.
The reciprocal of resistance R is called conductance G = 1/R and is measured in siemens (SI unit), sometimes referred to as a mho. Hence, siemens is the reciprocal of an ohm: . Although the concept of conductance is often used in circuit analysis, practical resistors are always specified in terms of their resistance (ohms) rather than conductance.
Electronic Symbols and Notations
The symbol used for a resistor in a circuit diagram varies from standard to standard and country to country. Two typical symbols are as follows.
American-style symbols. (a) resistor, (b) rheostat (variable resistor), and (c) potentiometer
IEC-style resistor symbol
The notation to state a resistor's value in a circuit diagram varies, too. The European notation avoids using a decimal separator, and replaces the decimal separator with the SI prefix symbol for the particular value. For example, 8k2 in a circuit diagram indicates a resistor value of 8.2 kΩ. Additional zeros imply tighter tolerance, for example 15M0. When the value can be expressed without the need for an SI prefix, an 'R' is used instead of the decimal separator. For example, 1R2 indicates 1.2 Ω, and 18R indicates 18 Ω. The use of a SI prefix symbol or the letter 'R' circumvents the problem that decimal separators tend to 'disappear' when photocopying a printed circuit diagram.
Theory of operation
The hydraulic analogy compares electric current flowing through circuits to water flowing through pipes. When a pipe (left) is filled with hair (right), it takes a larger pressure to achieve the same flow of water. Pushing electric current through a large resistance is like pushing water through a pipe clogged with hair: It requires a larger push (voltage drop) to drive the same flow (electric current).
The behavior of an ideal resistor is dictated by the relationship specified by Ohm's law:
Ohm's law states that the voltage (V) across a resistor is proportional to the current (I), where the constant of proportionality is the resistance (R).
Equivalently, Ohm's law can be stated:
This formulation states that the current (I) is proportional to the voltage (V) and inversely proportional to the resistance (R). This is directly used in practical computations. For example, if a 300 ohm resistor is attached across the terminals of a 12 volt battery, then a current of 12 / 300 = 0.04 amperes (or 40 milli amperes) occurs across that resistor.
Series and parallel resistors
In a series configuration, the current through all of the resistors is the same, but the voltage across each resistor will be in proportion to its resistance. The potential difference (voltage) seen across the network is the sum of those voltages, thus the total resistance can be found as the sum of those resistances:
As a special case, the resistance of N resistors connected in series, each of the same resistance R, is given by NR.
Resistors in a parallel configuration are each subject to the same potential difference (voltage), however the currents through them add. The conductances of the resistors then add to determine the conductance of the network. Thus the equivalent resistance (Req) of the network can be computed:
The parallel equivalent resistance can be represented in equations by two vertical lines "||" (as in geometry) as a simplified notation. Occasionally two slashes "//" are used instead of "||", in case the keyboard or font lacks the vertical line symbol. For the case of two resistors in parallel, this can be calculated using:
As a special case, the resistance of N resistors connected in parallel, each of the same resistance R, is given by R/N.
A resistor network that is a combination of parallel and series connections can be broken up into smaller parts that are either one or the other.
However, some complex networks of resistors cannot be resolved in this manner, requiring more sophisticated circuit analysis. For instance, consider a cube, each edge of which has been replaced by a resistor. What then is the resistance that would be measured between two opposite vertices? In the case of 12 equivalent resistors, it can be shown that the corner-to-corner resistance is 5⁄6 of the individual resistance. More generally, the Y-Δ transform, or matrix methods can be used to solve such a problem.
One practical application of these relationships is that a non-standard value of resistance can generally be synthesized by connecting a number of standard values in series or parallel. This can also be used to obtain a resistance with a higher power rating than that of the individual resistors used. In the special case of N identical resistors all connected in series or all connected in parallel, the power rating of the individual resistors is thereby multiplied by N.