Factors Affecting Resistance

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One of the most basic ideas in the study of electricity and current flow is resistance. A conductor‘s free electrons clash with the lattice structure’s fixed positive ions when an electric current flows through it. Resistance is the opposing force created by these collisions, which prevent electrons from moving freely.
Factors Affecting Resistance-Electrons
Electrons
Mathematically, resistance R is defined using Ohm’s law:
R = V / I
Where V is the potential difference across the conductor and I is the current through it.
Practically speaking, resistance is influenced by the material’s physical conditions in addition to its inherent qualities. We must investigate the elements influencing resistance in order to understand how it might be altered or managed.

Factors Affecting Resistance: Length of the Conductor

A conductor’s resistance is directly influenced by its length. A longer path for electrons to traverse is offered by longer conductors. Electrons lose energy when they collide with the material’s atoms several times while they are in motion.
* Observation: Resistance is directly proportional to the length of the conductor.  R α L
* Reason: Doubling the length doubles the number of collisions experienced by electrons.
* Example: A wire of length 2 meters has twice the resistance of a wire of 1 meter, provided both are made of the same material and have equal cross-sectional area.
This is why electrical transmission lines are made as short as possible or use materials with extremely low resistivity.
Factors Affecting Resistance-Electrical Transmission Lines
Electrical Transmission Lines

2.Cross-Sectional Area of the Conductor

The thickness (or area of cross-section) of the conductor plays an equally important role. A thicker wire provides more space for electrons to flow simultaneously, reducing the chances of collisions.
* Observation: Resistance is inversely proportional to the cross-sectional area. R  α  1 / A
* Reason: Larger area means more electrons can pass through without overcrowding, leading to smoother current flow.
* Example: A wire with twice the thickness (double area) has only half the resistance of a thinner wire.
Thus, heavy-duty electrical appliances like heaters or motors use thick copper wires to avoid overheating due to low resistance.
Factors Affecting Resistance-Motors
Motors
3. Nature of the Material: Different materials inherently offer different levels of opposition to current flow. This property is measured by resistivity (ῤ), which is an intrinsic property of the material.
* Conductors (like copper, silver, and aluminum) have low resistivity, meaning they allow easy flow of current.
* Insulators (like rubber, plastic, or wood) have very high resistivity, thus preventing the flow of current.
* Semiconductors (like silicon and germanium) have resistivity between conductors and insulators and are highly useful in modern electronics.
* Formula:  R = ῤ L / A
Here, the resistivity ῤ depends on the nature of the material and temperature.
* Example: Silver has the lowest resistivity among metals, but copper is more commonly used because it is cheaper and sufficiently conductive.

4. Temperature of the Conductor

The effect of temperature on resistance is vital.
* For metals: As temperature increases, the vibrations of atoms in the lattice also increase. This causes more frequent collisions of electrons, increasing resistance.
RT = R0 (1 + α ▲T)
Where α is the temperature coefficient of resistance.
* For alloys (like constantan, manganin): Resistance remains almost unchanged with temperature, which makes them suitable for making standard resistors.
* For semiconductors: Resistance decreases with an increase in temperature because more electrons gain energy to move to the conduction band, thereby increasing conductivity.
* Example: Filaments of electric bulbs (tungsten) have high resistance at elevated temperatures, allowing them to glow brightly.

5. Mechanical Stress and Strain

Stretching or compressing a conductor alters its resistance.
* When a wire is stretched, its length increases while cross-sectional area decreases. Since resistance is proportional to L / A, the resistance increases significantly.
* When compressed, length reduces, and cross-sectional area increases, lowering resistance.
This principle is applied in strain gauges, devices that measure tiny changes in strain by observing variations in resistance.

6. Impurities in the Material

The presence of impurities in a conductor changes its resistivity.
* Pure metals like copper and silver have very low resistivity. But when mixed with impurities, foreign atoms disrupt the flow of electrons, increasing collisions and hence resistance.
* Alloys are deliberately formed with controlled impurities to create a stable resistance even with temperature variations.
* Example: Adding nickel to copper increases resistivity, forming constantan, which is used in resistance wires.

7. Frequency of Current (AC)

For alternating current (AC), the concept of skin effect comes into play. At higher frequencies, current tends to concentrate near the surface of the conductor rather than uniformly throughout its cross-section.
* As a result, the effective cross-sectional area decreases, and the effective resistance increases.
* This effect is negligible for direct current (DC) but significant in high-frequency AC circuits.
8. Effects of Magnetism The electron’s route is changed in certain materials, particularly when a strong magnetic field is present. In magnetoresistance devices, this can lead to an increase in resistance and collisions.

Practical applications:

* Low resistance conductors (like copper and aluminum) are used for transmission.
* High resistance materials (like nichrome, constantan) are used in heating devices and resistors.
* Temperature-independent alloys ensure precise measurements in instruments.

Summary

A conductor’s resistance varies depending on its mechanical state, temperature, contaminants, material composition, length and area, and even the sort of current flowing through it.
The resistance of a conductor is given by:
R = ῤ L / A
Where R is resistance, ῤ is resistivity of the material, L is the length of the conductor, and A is its cross-sectional area.
 
Resistance is directly proportional to the length of the conductor. A longer conductor has more collisions of electrons with ions, hence greater opposition to current. Doubling the length doubles the resistance.
 
Thicker wires have larger cross-sectional area. Since resistance is inversely proportional to area, a thicker wire allows more electrons to flow simultaneously, reducing resistance.
 
* In metals, resistance increases with rise in temperature because atomic vibrations increase collisions.
* In semiconductors, resistance decreases with rise in temperature since more electrons gain energy to conduct.
 
Alloys have resistances that remain nearly constant with temperature (low temperature coefficient). This makes them stable and reliable for use in standard resistors and measuring instruments.
 
Impurities disturb the regular lattice structure of the conductor, increasing electron scattering and collisions. This raises the resistance. Controlled impurities are used in alloys to achieve desired resistance.
 
When a wire is stretched:
* Its length increases.
* Its cross-sectional area decreases.
Since R α L / A, the resistance increases significantly. This principle is used in strain gauges.

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