electrical resistance
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Electrical Resistance

 

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Electrical Resistance is one of the easiest aspects to understand - SOURCE

Resistance

For most materials, there is a simple relationship between the potential difference applied across two points and the current generated. An Ohmic material is one for which the potential difference and current are related as below:


 

Figure 9.4: Voltage vs. current for an Ohmic material

\begin{figure}
\begin{center}
\leavevmode
\epsfysize=6 cm
\epsfbox{figs/eandm-4.eps}
\end{center}
\end{figure}


For such materials the voltage and current are proportional - doubling the potential difference doubles the current. The constant of proportionality is called the resistance, which is defined through Ohm's law:



\fbox{\parbox{4.5in}{\vspace*{7pt}Voltage = Current x Resistance\vspace*{7pt}}}

The units of resistance are Volts / Ampères, or Ohms ($ \Omega$). Thus, for a given potential difference, materials with a high resistance will allow a small current relative to a material with a low resistance.

In analogy with heat resistance and conductivity, one can define an electrical conductivity as being proportional to the inverse of the resistance. Thus, good electrical conductors, such as copper, have a low resistance, and poor electrical conductors, such as concrete, have a high resistance.

At the atomic level, currents are pictured as the flow of the outer electrons of atoms through the material. Resistance then results from collisions of electrons with other electrons and with atoms. From this we would expect that raising the temperature of a material would increase the resistance, as the added heat energy would cause the electrons to move faster and hence collide more often. This is indeed what is generally observed.

Elementary Principles - SOURCE

Resistance

The electrical resistance of a circuit component or device is defined as the ratio of the voltage applied to the electric current whichflows through it:


If the resistance is constant over a considerable range of voltage, then Ohm's law, I = V/R, can be used to predict the behavior of the material. Although the definition above involves DC current and voltage, the same definition holds for the AC application of resistors.

Whether or not a material obeys Ohm's law, its resistance can be described in terms of its bulk resistivity. The resistivity, and thus the resistance, is temperature dependent. Over sizable ranges of temperature, this temperature dependence can be predicted from a temperature coefficient of resistance.

Conductors and insulators

Resistor combinations

Non-ohmic resistance: the electric pickle

AC behavior of resistor

Common carbon resistors

Index

DC Circuits

 

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Resistivity and Conductivity

The electrical resistance of a wire would be expected to be greater for a longer wire, less for a wire of larger cross sectional area, and would be expected to depend upon the material out of which the wire is made. Experimentally, the dependence upon these properties is a straightforward one for a wide range of conditions, and the resistance of a wire can be expressed as


The factor in the resistance which takes into account the nature of the material is the resistivity . Although it is temperature dependent, it can be used at a given temperature to calculate the resistance of a wire of given geometry.

The inverse of resistivity is called conductivity. There are contexts where the use of conductivity is more convenient.

Electrical conductivity = s = 1/r

Calculation

Table of resistivities

Common wire gauges

Microscopic view of resistivity

Index

 

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Resistor Combinations

The combination rules for any number of resistors in series or parallel can be derived with the use of Ohm's Law, the voltage law, and the current law.


Comparison example

Index

DC Circuits

 

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Resistivity Calculation

The electrical resistance of a wire would be expected to be greater for a longer wire, less for a wire of larger cross sectional area, and would be expected to depend upon the material out of which the wire is made (resistivity). Experimentally, the dependence upon these properties is a straightforward one for a wide range of conditions, and the resistance of a wire can be expressed as


Resistance = resistivity x length/area

For a wire of length L = m = ft
and area A = cm^2
corresponding to radius r = cm
and diameter inches for common wire gauge comparison
with resistivity = = x 10^ ohm meters
will have resistance R = ohms.

Enter data and then click on the quantity you wish to calculate in the active formula above. Unspecified parameters will default to values typical of 10 meters of #12 copper wire. Upon changes, the values will not be forced to be consistent until you click on the quantity you wish to calculate.


Standard wire gauges


Table of resistivities

The factor in the resistance which takes into account the nature of the material is the resistivity . Although it is temperature dependent, it can be used at a given temperature to calculate the resistance of a wire of given geometry.

Discussion

Table of resistivities

Common wire gauges

Index

 

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