Lecture 10: Electric Current and Circuits

PHYSICS 2140 - Lecture 10 Notes

Overview

• Date: October 10, 2022
• Topic: Electric Current and Circuits

Electric Current

• Definition of Electric Current:

  • Electric current is defined as the flow of electric charge over time.
  • This flow can be in the direction of positive charges or opposite to that of negative charges (electrons).

• Conventional Current Direction:

  • The direction of the current is considered to be the same as that of positive charge flow.

• Carriers of Current:

  • Charges in the current flow are referred to as 'carriers'.

• Formula for Current:

  • $I = \frac{\Delta q}{\Delta t}$
  • Where:
    • $I$ = Electric current (Amperes)
    • $\Delta q$ = change in electric charge (Coulombs)
    • $\Delta t$ = change in time (seconds)

• Unit of Current:

  • The standard unit of current is the Ampere (A), defined as:
  • $1 A = 1 C/s$
    • Where $C$ is Coulombs and $s$ is seconds.

Functioning of a Light Bulb

• Light Production:

  • A light bulb operates by transferring energy in the form of light and heat to the surrounding environment.
  • This energy is sourced from electric work, defined as the forced motion of electric charges (electrons) through a wire.

• Mechanism of Lighting:

  • As electrons move through the wire of the light bulb, they experience resistance (friction) which causes the wire to heat up and ultimately glow.

Causes of Electric Current

• Electric Field and Charge Movement:
  • An external electric field exerts force on charges present in a conductor.
  • When at equilibrium (charges not moving on average), the electric field inside a conductor is zero.
  • A conductor must have a non-zero electric field when current is present, meaning it is not at equilibrium.
  • The electric field is established due to a potential difference between the conductor's ends, directed from high potential to low potential.

Microscopic View of Current

• Random Motion of Electrons:

  • Electrons in a conductor exhibit random motion.
  • Average speed: Approximately $1000 ext{ km/s}$.
  • Collision events lead to random direction changes at very high frequencies.

• Average Velocity Without Electric Field:

  • The average velocity of electrons is zero in the absence of an external electric field, resulting in no net displacement over time.

• Average Velocity With Electric Field:

  • With an external electric field applied, electrons acquire a net displacement, averaging approximately $1 ext{ mm/s}$.

Drift Velocity

• Definition of Drift Velocity:

  • The average displacement over time of charge carriers is known as drift velocity ($v_d$).
  • As drift velocity increases, the current also increases.

• Charge Density:

  • Charge density ($n$) is defined as $n = \frac{N}{V}$,
  • Where:
    • $N$ = Number of carriers
    • $V$ = Volume of the medium.

• Current Density:

  • Describes how current is distributed over an area:
  • $J = \frac{I}{A}$
  • Related to drift velocity:
  • $I = q n A\Delta x/\Delta t = q n A v_d$

Resistance and Joule Heating

• Resistance:

  • Defined as the property of conductors that restricts the flow of current.
  • Resistance arises from electron collisions within the conductor with other particles (electrons, ions, etc).

• Joule Heating:

  • When electrons collide with other particles, energy is exchanged, increasing their kinetic energy and raising the thermal energy of the material.
  • This heat is dissipated to the environment as Joule heat.

Relationship of Current and Resistance

• Current-Resistance Relation:

  • Current (I) and resistance (R) are inversely proportional, meaning as resistance increases, current decreases.

• Dependence of Resistance:

  • The resistance of a conductor is influenced by its physical properties, particularly:
  1. Inversely proportional to the cross-sectional area (A). A larger area allows more room for charge flow, thus increasing current.
  2. Directly proportional to the length (L) of the conductor.

• Resistivity:

  • A material characteristic describes resistance, defined as:
  • $R = \frac{b q^2 n L}{A}$
  • Where $b$ is a coefficient relating to the material property and resistive forces on charges.

• Resistors:

  • Conductors that exhibit resistance are termed as resistors.

Ohm’s Law

• Ohm’s Law:
  • Expresses the relationship between current, voltage (potential difference), and resistance:
  • $I \propto \frac{1}{R}$
  • Therefore, $I = \frac{\Delta V}{R}$
  • Alternatively, as $\Delta V = I R$.

Additional Notes

• Practical Questions:
  • Inquiry into why electric bulb filaments are coiled and why electric stoves utilize coils can relate to concepts of resistance and heat conduction.