Electric current is the lifeblood of modern technology, powering our devices and enabling communication. It describes the flow of electric charge through conductors, driven by voltage differences. Understanding current is crucial for analyzing circuits and electromagnetic phenomena.

Current flow involves the movement of electrons in metals or ions in solutions. It's measured in amperes and follows Ohm's law, relating voltage and resistance. Current density, drift velocity, and power dissipation are key concepts that help us grasp how electricity behaves in various materials and devices.

Definition of electric current

• Electric current forms a fundamental concept in electromagnetism describing the flow of electric charge through a conductor
• Understanding electric current provides the foundation for analyzing circuits and electromagnetic phenomena in physics

Charge flow in conductors

• Occurs when free electrons move through a conductive material (metals, electrolytes)
• Driven by electric potential difference or electromotive force
• Measured in coulombs per second, equivalent to amperes (A)
• Analogous to water flow in pipes, with charge as the "fluid" and voltage as the "pressure"

Current direction conventions

• Conventional current flows from positive to negative terminals
• Electron flow moves in the opposite direction of conventional current
• Distinction arises from historical understanding before electron discovery
• Both conventions used in different contexts, important to specify which is being used

Microscopic model of current

Drift velocity of electrons

• Average velocity of charge carriers in response to an electric field
• Typically much slower than the random thermal motion of electrons
• Calculated using the formula $v_d = \frac{I}{nAq}$, where I is current, n is charge carrier density, A is cross-sectional area, and q is charge per carrier
• Explains why electrical signals propagate near the speed of light while electrons move slowly

Current density

• Vector quantity describing current flow per unit area
• Expressed as $J = nqv_d$, where n is charge carrier density, q is charge per carrier, and v_d is drift velocity
• Relates to total current by $I = \int J \cdot dA$ over the cross-sectional area
• Used in analyzing non-uniform current distributions in conductors

Ohm's law

Resistance vs conductance

• Resistance (R) opposes current flow, measured in ohms (Ω)
• Conductance (G) facilitates current flow, measured in siemens (S)
• Relationship given by $G = \frac{1}{R}$
• Ohm's law states $V = IR$ or $I = GV$, linking voltage, current, and resistance/conductance

Temperature effects on resistance

• Most metals increase resistance with temperature due to increased lattice vibrations
• Semiconductors generally decrease resistance with temperature due to increased charge carriers
• Temperature coefficient of resistance (α) quantifies this effect: $R = R_0[1 + α(T - T_0)]$
• Superconductors exhibit zero resistance below a critical temperature

Electrical power

Power in resistive circuits

• Power (P) represents the rate of energy transfer in a circuit
• In resistive elements, $P = VI = I^2R = \frac{V^2}{R}$
• Measured in watts (W), equivalent to joules per second
• Determines energy consumption and heat generation in electrical devices

Joule heating

• Also known as resistive or ohmic heating
• Occurs when electric current passes through a resistor
• Power dissipated as heat given by $P = I^2R$
• Utilized in electric heaters, incandescent bulbs, and fuses
• Can be detrimental in high-power electronics, requiring cooling systems

Direct vs alternating current

DC sources and applications

• Constant polarity and usually constant magnitude over time
• Provided by batteries, solar cells, and DC power supplies
• Used in low-voltage electronics, LED lighting, and some transportation systems
• Allows for efficient energy storage in batteries and capacitors

AC characteristics and frequency

• Periodically reverses direction and oscillates in magnitude
• Characterized by frequency (typically 50 or 60 Hz in power grids)
• Enables efficient long-distance power transmission through transformers
• Described by sinusoidal function: $I(t) = I_0 \sin(2πft)$, where I_0 is peak current and f is frequency

Current in different circuit elements

Current through resistors

• Follows Ohm's law: $I = \frac{V}{R}$
• Current and voltage are in phase for pure resistors
• Power dissipation occurs as heat
• Used for current limiting and voltage division in circuits

Current through capacitors

• Current leads voltage by 90° in ideal capacitors
• Governed by the relationship $I = C\frac{dV}{dt}$
• No DC current flows through a fully charged capacitor
• AC current depends on frequency: $I = 2πfCV$ for sinusoidal voltage

Current through inductors

• Current lags voltage by 90° in ideal inductors
• Described by $V = L\frac{dI}{dt}$
• Opposes changes in current flow
• AC current depends on frequency: $I = \frac{V}{2πfL}$ for sinusoidal voltage

Kirchhoff's current law

Junction rule

• States that the sum of currents entering a junction equals the sum of currents leaving it
• Mathematically expressed as $\sum I_{in} = \sum I_{out}$
• Based on the principle of charge conservation
• Applies to both DC and AC circuits at any instant

Applications in circuit analysis

• Used to set up equations for solving complex circuit problems
• Enables determination of unknown currents in multi-loop circuits
• Combined with Kirchhoff's voltage law for complete circuit analysis
• Essential for analyzing parallel circuits and current dividers

Measuring electric current

Ammeters and their use

• Connected in series with the circuit element being measured
• Ideally have zero resistance to avoid affecting the circuit
• Digital ammeters use analog-to-digital converters for precise readings
• Range selection important to avoid damage from overcurrent

Safety considerations

• Never connect an ammeter in parallel with a voltage source
• Use fused leads to protect against accidental overcurrent
• Ensure proper insulation and grounding when working with high currents
• Be aware of the maximum current rating of the ammeter and circuit components

Current density and continuity

Current density vector

• Represents current flow per unit area at a point in a conductor
• Defined as $\vec{J} = \sigma \vec{E}$, where σ is conductivity and E is electric field
• Measured in amperes per square meter (A/m²)
• Used in analyzing non-uniform current distributions in conductors

Continuity equation

• Expresses conservation of electric charge in differential form
• Given by $\nabla \cdot \vec{J} + \frac{\partial \rho}{\partial t} = 0$, where ρ is charge density
• Relates spatial variation of current density to time rate of change of charge density
• Fundamental in electromagnetic theory and plasma physics

Superconductivity

Zero resistance phenomenon

• Occurs in certain materials below a critical temperature
• Results from electron pairing (Cooper pairs) and quantum effects
• Characterized by perfect diamagnetism (Meissner effect)
• Discovered in mercury by Kamerlingh Onnes in 1911

Applications of superconductors

• Used in creating powerful electromagnets for MRI machines and particle accelerators
• Enables highly efficient power transmission with minimal losses
• Applied in sensitive magnetic field detectors (SQUIDs)
• Potential for future use in quantum computing and high-speed maglev trains

Electrolytic conduction

Ionic current in solutions

• Charge carried by movement of ions in electrolyte solutions
• Depends on ion concentration, mobility, and applied electric field
• Follows Faraday's laws of electrolysis
• Important in batteries, electroplating, and electrochemical sensors

Faraday's laws of electrolysis

• First law states mass of substance deposited is proportional to the quantity of electricity passed
• Second law relates the masses of different substances deposited by the same quantity of electricity
• Expressed mathematically as $m = \frac{QM}{zF}$, where Q is charge passed, M is molar mass, z is valence number, and F is Faraday constant
• Fundamental to electrochemistry and quantitative analysis

Semiconductor current

Electron vs hole current

• Electrons in conduction band and holes in valence band contribute to current flow
• Total current is sum of electron and hole currents: $I_{total} = I_e + I_h$
• Mobility of electrons generally higher than holes in most semiconductors
• Relative contribution depends on doping type and concentration

Doping effects on conductivity

• Introduces extra charge carriers (electrons or holes) into the semiconductor
• N-type doping increases electron concentration, p-type increases hole concentration
• Dramatically alters conductivity and current-voltage characteristics
• Enables creation of diodes, transistors, and other semiconductor devices

Plasma currents

Ionized gas conduction

• Occurs in partially or fully ionized gases (plasmas)
• Involves movement of both electrons and ions
• Governed by complex interactions between charged particles and electromagnetic fields
• Exhibits non-linear behavior and collective effects

Applications in technology

• Used in plasma displays and lighting (fluorescent lamps)
• Employed in plasma cutting and welding in manufacturing
• Crucial in fusion energy research (tokamaks, stellarators)
• Applied in space propulsion systems (ion engines, plasma thrusters)

Biological electric currents

Nerve impulses

• Propagate along neurons through action potentials
• Involve rapid changes in membrane potential due to ion channel activity
• Typically have amplitudes of about 100 mV and durations of 1-2 ms
• Essential for information transmission in the nervous system

Electrocardiograms and brain activity

• ECG measures electrical activity of the heart over time
• EEG records electrical activity of the brain through scalp electrodes
• Both utilize sensitive current and voltage measurements
• Provide crucial diagnostic information in medicine and neuroscience

Current in electromagnetic fields

Displacement current

• Introduced by Maxwell to explain electromagnetic wave propagation
• Occurs in changing electric fields, even in absence of conduction current
• Given by $I_d = ε_0 \frac{dΦ_E}{dt}$, where ε_0 is permittivity of free space and Φ_E is electric flux
• Essential for understanding capacitor behavior and electromagnetic radiation

Maxwell's equations and current

• Ampère's law with Maxwell's correction includes displacement current
• Curl of magnetic field related to sum of conduction and displacement currents
• Enables prediction of electromagnetic waves and their properties
• Unifies electric and magnetic phenomena in a complete theory of electromagnetism