Electrical resistance and conductance
Fundamental electrical properties quantifying opposition and ease of current flow.
Electrical resistance quantifies how strongly an object opposes the flow of electric current, while its reciprocal, electrical conductance, measures how easily current passes. This opposition shares conceptual parallels with mechanical friction. The SI unit for resistance is the ohm (Ω), and for conductance, the siemens (S). Resistance depends largely on the object’s material: insulators like rubber have very high resistance and low conductance, whereas conductors like metals exhibit very low resistance and high conductance. This relationship is formalized through the material properties of resistivity and conductivity. However, resistance and conductance are extensive properties, also influenced by an object’s size and shape. For instance, a long, thin wire has higher resistance than a short, thick one made of the same material. All objects resist current except superconductors, which have zero resistance.
The resistance \( R \) of an object is defined as the ratio of voltage \( V \) across it to current \( I \) through it, with conductance \( G \) as its reciprocal: \( R = V/I \) and \( G = I/V \). For many materials and conditions, \( V \) and \( I \) are directly proportional, making \( R \) and \( G \) constant for a given object (though dependent on geometry, material, temperature, or strain). This proportionality is Ohm’s law, and materials obeying it are called ohmic. In non-ohmic devices—such as transformers, diodes, incandescent bulbs, or batteries—\( V \) and \( I \) are not proportional. Here, the ratio \( V/I \) is still useful as chordal (or static) resistance, corresponding to the slope of a chord from the origin on the I–V curve. Alternatively, the derivative \( dV/dI \) defines differential resistance, useful in certain analyses.
- SI unit of resistance
- ohm (Ω)
- SI unit of conductance
- siemens (S)
- Key relationship
- R = V/I, G = I/V = 1/R
- Factors affecting resistance
- material, length, cross-sectional area, temperature, strain
- Ohmic materials
- materials where V and I are directly proportional
Lore & Background
The electrical resistance of an object quantifies its opposition to the flow of electric current, while its reciprocal, conductance, measures the ease with which current passes. The SI unit of resistance is the ohm (Ω), and conductance is measured in siemens (S). Resistance shares conceptual parallels with mechanical friction. The resistance of an object depends primarily on the material it is made of. Objects made of electrical insulators, such as rubber, typically exhibit very high resistance and low conductance, whereas objects made of electrical conductors, like metals, display very low resistance and high conductance. This material dependency is quantified by the properties of resistivity and conductivity. However, material is not the sole factor; resistance and conductance are extensive properties, meaning they also depend on an object’s size and shape. For instance, a long, thin wire has higher resistance than a short, thick wire of the same material. All objects resist electric current except for superconductors, which have zero resistance. Resistance is defined as the ratio of voltage across an object to the current through it, with conductance being the reciprocal of this ratio. For many materials and conditions, voltage and current are directly proportional, making resistance and conductance constant values for a given object, a relationship known as Ohm’s law. Materials satisfying this are called ohmic. In other cases, such as transformers, diodes, incandescent light bulbs, or batteries, voltage and current are not directly proportional. Here, the ratio of voltage to current is termed chordal or static resistance, while the derivative of voltage with respect to current is called differential resistance.
Reader's Guide
Electrical resistance and conductance are defined by the ratio of voltage to current and its reciprocal, respectively. For many materials, voltage and current are directly proportional (Ohm's law), making resistance constant for a given object. This proportionality holds for ohmic materials like wires and resistors. In non-ohmic devices such as diodes or transformers, the ratio varies, leading to concepts like chordal resistance or differential resistance. The resistance of a uniform conductor can be calculated from its length, cross-sectional area, and material resistivity. These principles are essential for designing circuits and understanding how components behave under different conditions.
Did You Know?
- Electrical resistance is measured in ohms (Ω), while conductance is measured in siemens (S).
- Superconductors have a resistance of zero.
- A wire's resistance is higher if it is long and thin, and lower if it is short and thick.
- Ohm's law states that for ohmic materials, voltage and current are directly proportional.
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