Lecture Notes 26 Dr Merabet

Chapter 26: Current and Resistance

26.1 Electric Current

Electric current is defined as the flow of charges between two points in space, driven by a potential difference.

  • Flow of Charge:

    • Net flow of charge exists when there is a potential difference between two points.

    • Analogy: The flow of water in a pipe is driven by a pressure difference, similar to how current is driven by voltage. The current can be quantified similarly to water flow, by measuring how much charge passes through a certain area over time.

More specifically, when charges move perpendicular to the surface area A (like in a wire), the average current (I) can be defined as:

  • I = Q / Δt Where:

    • Q = the charge that flows through the area A in the time interval Δt.

    • The direction of current flows in the direction of positive charge movement, even though in conductors it is typically electrons that move negatively.

26.2 Resistance

Resistance is a property of materials that quantifies how strongly they oppose the flow of electric current.

  • Ohm's Law:


    • States that the current density (J) is proportional to the electric field (E), described by the formula:J = σE

    • The ratio of the current density to the electric field is the conductivity (σ), and materials that follow this relationship are termed ohmic materials.

  • Defining Resistance:

    • Resistance (R) of a conductor is related to potential difference (V) and current (I) by: R = V / I

    • SI unit of resistance is the ohm (Ω), equivalent to one volt per ampere.

Resistance and Material Properties

  • Different materials have unique resistivities, with metals generally being good conductors (low resistivity) and insulators (high resistivity) like glass and rubber.

  • The resistivity of various materials varies with temperature, typically showing linear behavior over limited temperature ranges. A table of resistivities and temperature coefficients for common materials is provided for reference.

26.3 A Model for Electrical Conduction

The Drude model describes electrical conduction within metals:

  • Assumes conduction electrons behave like a gas of free particles that undergo random collisions, leading to drift motion when an electric field is applied.

  • Drift Velocity (Vd) represents the average speed of these charge carriers in response to an electric field, and can be expressed in relation to the current.

26.4 Resistance and Temperature

  • Resistance increases with temperature in most conductors; however, some materials may exhibit a decrease in resistance with rising temperature.

  • The behavior of resistance with temperature can be expressed mathematically, allowing for calculations of how resistance changes over a specified range.

26.5 Superconductors

Superconductivity is a phenomenon where resistance drops to zero below a certain critical temperature (T_c).

  • This discovery enables applications in technologies requiring high efficiency and low energy loss.

26.6 Electrical Power

Power in electrical circuits can be understood as the rate at which electric potential energy is transferred to devices like lightbulbs:

  • The formula for electrical power (P) delivered to a resistor is: P = IV = I^2R = V^2/R Where:

    • I = current

    • V = potential difference

    • R = resistance

Example calculations provided illustrate practical uses of this equation in electrical heating and energy consumption over time.