Lesson 1: Fundamentals of Circuit Theory
Recommended Article : [Circuit Theory] Circuit Theory Table of Contents
1. Terminology Describing Electric Phenomena
3. Concentrated Constant System and Distributed Constant System
4. Linear Systems and Binary Systems
1. Terminology Describing Electric Phenomena
⑴ Charge
① Definition : Fundamental property causing electric phenomena
② Types of charge : Positive and negative charges; like charges repel, unlike charges attract
○ Difference from gravity is in having only one polarity
③ Amount of charge : Measurement of charge magnitude
○ Unit : Coulomb (C)
○ Charge of one electron : -1.6 × 10-19 C
○ Number of electrons in 1 C : 6.25 × 1018
○ Coulomb’s constant and Avogadro’s number (6.02 × 1023) are unrelated
○ Charge of 1 mole of electrons = (6.02 × 1023) × (1.6 × 10-19) = 96,485 C
○ Small size of fundamental charge allows for continuous consideration of charge
④ Copper at 20 ℃ has electron density of 1023 electrons/cm3
⑤ Separation of charges creates voltage, and flow of charges creates current
⑵ Electric Current
① Definition : Net flow of charged particles per unit time, such as electrons or ions
○ Conductors or wires : Allow free electrons to flow as current
○ Electrolytes : Allow charged ions to flow as current
○ Vacuum tubes (discharge tubes) : Allow flow of positive ions and electrons as current
○ Unit : C/s = A
② Direction of Current
○ Movement of charges : Electrons move when a force is applied, nuclei remain fixed
○ Direction of current : (+) → (-)
○ Direction of free electrons : (-) → (+)
○ Direction of positive charges : (+) → (-)
③ Type 1. Drift Current
○ Definition : Movement of free electrons due to electric field in a conductor
○ Electrons are more mobile than positive holes
○ Ohm’s law applies to drift current only
○ Application : Field-effect transistors (FET)
④ Type 2. Convection Current or Diffusion Current
○ Definition : Current due to movement or diffusion of charged particles like electrons, positive holes, or ions
○ Notable in vacuum or rarefied gases
○ Application : PN junction diodes, bipolar junction transistors (BJT), cathode-ray tubes, vacuum tubes
⑤ Type 3. Polarizing Current : Time-dependent variation of polarization charge
⑥ Type 4. Displacement Current : Time-dependent variation in charge density, not carried by actual charge carriers
⑶ Electric Potential
① Electric Field : Magnitude of electric force per unit charge
② Electric Potential : Electric potential energy per unit charge
③ Voltage : Energy required to separate charges per unit charge (Unit : J/C = V)
④ Relation between Electric Field and Electric Potential in Uniform Field
⑤ Electric field is represented by slope of potential-distance graph
⑷ Power : Rate of work done by an electrical device, 1 horsepower (hp) = 735 W
① Power in a Resistor
② Power in an Electric Motor
③ Sign of Power
○ Positive value : Energy is delivered to circuit component
○ Negative value : Energy is dissipated from circuit component
④ Tip: Power in a resistor is always positive
○ i.e., when current flows, it’s positive power; when opposite, it’s negative power
○ Note that this is a matter of definition rather than actual sign
Figure. 1. Rule for Sign of Power in a Resistor
⑤ According to the Law of Energy Conservation, the sum of powers in any circuit is 0
⑸ Other Terminology
① Short Circuit
② Open Circuit
③ Node
④ Branch
2. Maxwell’s Equations
⑴ Maxwell’s First Equation: Gauss’s Law for Electricity
① Mathematical Expression : Using Divergence Theorem
② D is electric flux density
⑵ Maxwell’s Second Equation: Gauss’s Law for Magnetism (Law of Magnetic Conservation)
① Mathematical Expression : Using Divergence Theorem
② Physical Interpretation : No magnetic monopoles
③ μH is magnetic flux density
⑶ Maxwell’s Third Equation: Ampere’s Circuital Law
① Mathematical Expression : Using Green’s Theorem
② Physical Interpretation
○ Current or virtual current leads to the generation of a magnetic field around the region
○ Direction of magnetic field follows the right-hand screw rule with respect to current direction
⑷ Maxwell’s Fourth Equation: Faraday’s Law of Electromagnetic Induction
① Mathematical Expression : Using Green’s Theorem
② Physical Interpretation : Change in magnetic flux across any closed loop induces a current in the loop
⑸ Law of Charge Conservation (Continuity Equation for Charge)
① Mathematical Expression : Using Divergence Theorem
② Physical Interpretation
○ Related to definition of current
○ Total net charge in the universe is 0
3. Concentrated Constant System and Distributed Constant System
⑴ Concentrated Constant System
① All parts of the system sense external physical quantities simultaneously for rigid bodies
② Application of KCL, KVL, V-I characteristics is possible
⑵ Distributed Constant System
① All parts of the system do not experience the same physical quantities simultaneously for flexible bodies
② Interpretation only possible through numerical analysis
⑶ Criteria for Judgment
① If the propagation time for a wave through the system is much smaller than the period of external sources, it’s a concentrated constant system
② Example : If the system’s characteristic length is comparable to the size of a lab, and the frequency of the power supply is 60 Hz
4. Linear Systems and Binary Systems
⑴ Linear System
① Definition : Relates input to output in a linear approximation at a given operating point
② Examples : Resistors, capacitors, inductors, diodes, transistors
⑵ Binary System
① Definition : Relates input to output in terms of all-or-none principle, i.e., using 1 or 0
② Examples : Logic gates
Input : 2015.12.23 21:01
Modification : 2022.09.11 11:53