Current Electricity: Electric Charges in Motion

Current Electricity

Introduction to Current Electricity

Current electricity is the study of electric charges in motion and the associated energies. It forms the basis for understanding how electrical circuits function and how energy is transferred in electrical systems.

• Electricity: The study of electric charges and their associated energies.

• Current: The flow of electric charges along a conductor in a specific direction.

• Conventional current: Defined as the flow of positive charges; in reality, electrons (negatively charged particles) move in the opposite direction to the conventional current.

• Electric conductors: Materials that allow an easy flow of electric charge (e.g., metals).

• Electric insulators: Materials that do not allow electric charge to flow easily (e.g., rubber, glass).

• Alternating current (AC): Current that reverses direction periodically.

• Direct current (DC): Current that flows in one direction only.

Electric Current

Definition and Measurement

Electric current is the rate of flow of electric charge along a conductor. It is a fundamental quantity in electrical circuits.

• Electric current (I): Defined as $I = \frac{dQ}{dt}$, where $Q$ is the electric charge and $t$ is time.

• Unit of current: The SI unit is the ampere (A), where $1\ \text{A} = 1\ \text{Coulomb/second}$.

• Direction: By convention, current is considered as the flow of positive charge (conventional current direction).

• Example: If a current of 450 mA flows for 13 minutes, the total charge $Q$ passing through a cross-section is $Q = I \Delta t$.

Potential Difference

Definition and Role in Circuits

For current to flow in a circuit, there must be a potential difference (voltage) between two points. This potential difference is provided by sources such as batteries and generators.

• Electric potential (V): The electric potential energy per unit charge at a point.

• Potential difference (V): The difference in electric potential between two points; drives the flow of current.

• Energy supply: Batteries and generators supply energy to maintain the potential difference in a circuit.

• Charge movement: Positive charges move from the positive terminal to the negative terminal of a battery (conventional direction), while electrons move from negative to positive.

Resistance and Resistivity

Definitions and Relationships

Resistance and resistivity are properties that describe how materials oppose the flow of electric current.

• Resistance (R): The opposition to the flow of electric current, measured in ohms ($\Omega$).

• Formula: $R = \rho \frac{L}{A}$, where $\rho$ is resistivity, $L$ is the length of the conductor, and $A$ is the cross-sectional area.

• Resistivity ($\rho$): A material property that quantifies how strongly a material opposes current flow; SI unit is $\Omega \cdot \text{m}$.

• Temperature dependence: The resistivity of most materials decreases with decreasing temperature.

Resistivity of Some Materials at Room Temperature

The following table compares the resistivity of common materials:

Material	Resistivity, $\rho$ ($\Omega \cdot \text{m}$)	Material	Resistivity, $\rho$ ($\Omega \cdot \text{m}$)
Copper	$1.72 \times 10^{-8}$	Iron	$9.71 \times 10^{-8}$
Silver	$1.65 \times 10^{-8}$	Tungsten	$5.49 \times 10^{-8}$
Aluminium	$2.82 \times 10^{-8}$	Gold	$2.44 \times 10^{-8}$
Mercury	$20.6 \times 10^{-8}$	Lead	$22.0 \times 10^{-8}$

Additional info: Table values are standard for room temperature; actual values may vary with temperature and purity.

• Example: For an aluminium wire of length $8.5\ \text{km}$ and cross-sectional area $5.2 \times 10^{-4}\ \text{m}^2$, the resistance is $R = \rho \frac{L}{A}$.