Electrical resistance and conductance

Electrical Resistance and Conductance

Hydraulic analogy of resistance

Electrical resistance and conductance are fundamental concepts in the field of electricity and electronics. They describe how electric current flows through a material and how easily it can pass through a given circuit element.

Definition

Electrical resistance is a measure of the opposition to the flow of electric current through a conductor. It is denoted by the symbol \( R \) and is measured in ohms (\( \Omega \)). The higher the resistance, the more difficult it is for current to flow through the material.

Electrical conductance, on the other hand, is the reciprocal of resistance. It measures how easily electric current can flow through a conductor. Conductance is denoted by the symbol \( G \) and is measured in siemens (S).

Ohm's Law

Ohm's law is a fundamental principle that relates voltage (\( V \)), current (\( I \)), and resistance (\( R \)) in an electrical circuit. It is expressed as:

\[ V = I \times R \]

This equation shows that the voltage across a conductor is directly proportional to the current flowing through it, with the resistance being the constant of proportionality.

Factors Affecting Resistance

Metal film resistor

The resistance of a material depends on several factors:

• Material: Different materials have different intrinsic resistivities. Metals, for example, generally have low resistivity, while insulators have high resistivity.
• Length: The longer the conductor, the higher the resistance.
• Cross-sectional area: A larger cross-sectional area results in lower resistance.
• Temperature: For most materials, resistance increases with temperature.

Resistivity

Geometry affecting resistivity

Resistivity is a property of a material that quantifies how strongly it resists electric current. It is denoted by the symbol \( \rho \) and is measured in ohm-meters (\( \Omega \cdot m \)). The resistance \( R \) of a uniform conductor can be calculated using the formula:

\[ R = \rho \frac{L}{A} \]

where \( L \) is the length of the conductor and \( A \) is its cross-sectional area.

Conductance and Conductivity

Conductance is the ease with which electric current flows through a conductor. It is related to conductivity, which is the reciprocal of resistivity. Conductivity is denoted by \( \sigma \) and is measured in siemens per meter (S/m).

Non-linear and Differential Resistance

IV curves showing different types of resistance

In some materials and devices, the relationship between voltage and current is not linear. This is known as non-linear resistance. Devices such as diodes and transistors exhibit non-linear resistance characteristics.

Differential resistance is the change in voltage divided by the change in current at a particular point on the IV curve. It is important in analyzing non-linear devices.

Negative Differential Resistance

Negative differential resistance

Negative differential resistance occurs when an increase in voltage across a device leads to a decrease in current. This phenomenon is used in certain electronic components like tunnel diodes.

Measurement of Resistance

Multimeter measuring resistance

Resistance can be measured using a multimeter, which applies a known voltage to a resistor and measures the current flowing through it to calculate the resistance using Ohm's law.

Applications

Cartridge heater

Resistance is a critical parameter in designing electrical circuits. Resistors are used to control current flow, divide voltages, and protect components from excessive current.

Related Pages

• Ohm's law
• Resistor
• Conductivity
• Semiconductor
• Insulator (electricity)