What Is Electrical Resistance?

Resistance is a fundamental property of materials that opposes the flow of electric current. It determines how much a material restricts the movement of electric charges when a potential difference is applied across its ends. Resistance plays a critical role in analyzing and designing electrical circuits.

Definition and Nature of Resistance

Resistance refers to the property of a material that restricts the flow of electric charge. It arises due to the collision of electrons with atoms within a conductor, which impedes electron movement and causes energy dissipation as heat.

The SI unit of resistance is the ohm ($\Omega$). If a conductor has a resistance of one ohm, a current of one ampere flows through it when a potential difference of one volt is applied across its ends.

Ohm’s Law and Resistance

Ohm’s Law states that the electric current ($I$) flowing through a conductor between two points is directly proportional to the potential difference ($V$) across the two points at constant temperature.

Mathematically, Ohm’s Law is expressed as $V = IR$, where $R$ is the resistance. This relationship enables the determination of resistance using measurable circuit quantities.

For further information on this relationship and its implications, refer to Ohm's Law and Resistance.

Mathematical Expression for Resistance

The resistance $R$ of a uniform conductor is given by the relation $R = \rho \dfrac{L}{A}$, where $\rho$ is the resistivity of the material, $L$ is the length, and $A$ is the cross-sectional area of the conductor.

This formula shows that resistance increases with length and decreases with cross-sectional area. Material-specific resistivity further determines how much resistance the conductor offers.

Detailed differences between resistance and resistivity can be found at Resistance vs Resistivity.

Types of Materials Based on Resistance

Materials can be classified on the basis of their resistance into conductors, insulators, and semiconductors. Conductors have low resistance and allow significant current flow, whereas insulators exhibit very high resistance and impede current.

• Conductors: Low resistance, e.g., copper
• Insulators: High resistance, e.g., glass
• Semiconductors: Intermediate resistance

For an introduction to current electricity and its interaction with resistance, visit Current Electricity Fundamentals.

Factors Affecting Resistance

Several factors influence the resistance of a conductor. The most significant factors are:

• Length of the conductor (directly proportional)
• Cross-sectional area (inversely proportional)
• Nature of material (resistivity)
• Temperature of the conductor

As temperature increases, the resistance of most metallic conductors also increases, while that of semiconductors usually decreases.

Dimensional Formula of Resistance

The dimensional formula of resistance is derived from Ohm’s Law. The potential difference $V$ has dimensions $[M^1L^2T^{-3}I^{-1}]$ and electric current $I$ has $[I^1]$. Therefore,

$R = \dfrac{V}{I}$ has dimensions $[M^1L^2T^{-3}I^{-2}]$.

Resistivity and Its Relation to Resistance

Resistivity ($\rho$) is an intrinsic property of a material that quantifies how strongly it opposes current flow. It is independent of the shape and size of the material but depends on temperature and the material’s nature.

The resistance $R$ can be related to resistivity as $R = \rho \dfrac{L}{A}$. The SI unit of resistivity is ohm-metre ($\Omega\,\text{m}$).

Measurement of Resistance

Resistance in a circuit is commonly measured using an ohmmeter or a multimeter. Direct measurement is conducted in an open circuit, as the presence of current influences measurement accuracy.

Alternatively, resistance can be determined indirectly using Ohm’s Law, by measuring voltage and current and applying $R = \dfrac{V}{I}$ in a circuit.

Applications and Practical Importance of Resistance

Resistance is utilized in designing electronic circuits to control current flow. High-resistance elements convert electrical energy into heat, as in heaters and filament bulbs, while low-resistance conductors are used for efficient power transmission.

Repeated use of combinations of resistors in circuits allows for the regulation and division of current. For more details, refer to Combination of Resistors.

Calculation Example: Circuit Resistance Using Ohm’s Law

If a wire has a resistance of $R$, and a potential difference $V$ is applied across it, the current $I$ is $I = \dfrac{V}{R}$. For example, if $V = 10\,\text{V}$ and $R = 5\,\Omega$, then $I = 2\,\text{A}$.

Equivalent Resistance in Circuits

When multiple resistors are connected in a circuit, the total or equivalent resistance depends on the configuration. In series, the resistances add: $R_{eq} = R_1 + R_2 + \ldots$. In parallel, $1/R_{eq} = 1/R_1 + 1/R_2 + \ldots$.

A structured explanation is available at Understanding Equivalent Resistance.

Summary Table: Resistance vs Resistivity

A detailed discussion separating resistance from resistivity is found at Resistance vs Resistivity.