Current, Resistance, and Electromotive Force (EMF)

Introduction to Electric Circuits

Electric circuits are fundamental to modern technology, enabling the controlled flow of electric charge to power devices from flashlights to industrial systems. Understanding how current, resistance, and electromotive force interact is essential for analyzing and designing electrical systems.

• Electric circuits contain charges in motion, which transfer energy as they move through components like light bulbs.

• The energy of the charges decreases as current passes through resistive elements, such as bulbs, due to energy dissipation (usually as heat or light).

• Electric circuits are integral to devices such as computers, televisions, and power systems.

Electric Current

Definition and Description

Electric current is the rate at which electric charge passes through a given area. It is a fundamental quantity in circuit analysis and is measured in amperes (A).

• Current (I) is defined as the rate of flow of charge:

• Where is the electric charge and is time.

• In a conductor, current is due to the movement of charge carriers (such as electrons in metals).

• The drift speed () is the average velocity of charge carriers due to an electric field.

• For a conductor with charge carriers per unit volume, each with charge , and cross-sectional area :

• This equation relates current to the microscopic properties of the conductor.

Direction of Current Flow

Current can be produced by the flow of either positive or negative charges. However, by convention, the direction of current is defined as the direction in which positive charges would move.

• Conventional current flows from higher to lower electric potential, as if positive charges are moving.

• In metallic conductors, the actual charge carriers are electrons (negative), but current direction is still defined as the direction positive charges would move.

Current Density

The current density () is a vector quantity that describes the amount of current flowing per unit area, and its direction is the same as the drift velocity of positive charge carriers.

• Current density is given by:

• Where is the number density of charge carriers, is the charge per carrier, and is the drift velocity.

• The direction of is always the same as the electric field, regardless of the sign of the charge carriers.

Types of Charge Carriers

In conductors, current can be carried by different types of charged particles, depending on the material.

• In metals, electrons are the primary charge carriers.

• In ionic solutions (e.g., sodium chloride in water), both positive ions (cations) and negative ions (anions) contribute to the total current.

• The total current is the sum of the currents due to each type of charge carrier.

Summary Table: Key Quantities in Electric Current

Example: Current in a Copper Wire

• A copper wire with a diameter of 1.02 mm carries a current of 1.67 A. The free-electron density is electrons/m3.

• To find the current density ():

• To find the drift speed ():

• This drift speed is much slower than the random thermal speed of electrons.