Circuit Craziness
These are the three classic passive components that store or dissipate energy in a system.
What are resistors, inductors, and capacitors?
This mathematical tool allows circuit differential equations to be solved as simpler algebraic problems.
What are complex numbers
This local expression, ∇⋅j+∂tρ=0, represents the fundamental conservation of charge.
What is the continuity equation
Calculated as 1/μ0ϵ0, this is the universal speed at which electromagnetic signals propagate in a vacuum
What is the speed of light (c)?
This fundamental law of electrostatics states that the force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance separating them
What is Coulomb’s Law?
In the mechanical analogy of an LC circuit, this component acts like a spring, storing energy even when no charge is in motion.
What is a capacitor?
Measured in Ohms, this is the complex generalized version of resistance in an AC circuit
What is impedance (Z)?
This term, ϵ0∂tE, acts as a continuation of current density even in the absence of physical charge carriers.
What is the displacement current?
Defined as S=1/μ0(E×B), this vector field represents the flow of energy per unit time per unit area.
What is the Poynting vector?
This essential law relates the net electric flux passing through a closed surface to the total quantity of charge enclosed within that surface
What is Gauss’s Law?
This component provides a circuit with "inertia," resisting changes in current and associating energy with charges in motion.
What is an inductor?
This is the specific phase shift, in degrees, that a purely inductive circuit has between its voltage and current.
What is 90 degrees (or π/2)?
This specific law of induction states that a changing magnetic field is associated with a curling electric field.
What is Faraday's Law?
In a traveling EM wave in a vacuum, this is the constant ratio between the magnitude of the Electric field and the Magnetic field (E/B).
What is the speed of light (c)?
Often summarized by a minus sign in Faraday’s Law, this principle dictates that an induced current will flow in a direction that creates a magnetic field opposing any change in magnetic flux
Answer: What is Lenz’s Law?
In an AC circuit, this frequency-dependent state occurs when the inductive and capacitive effects cancel out, resulting in the maximum peak current.
What is resonance?
This theorem states that maximum power is delivered to a load when the load impedance is the complex conjugate of the source impedance.
What is the Maximum Power Transfer Theorem?
Without free charges or currents, Maxwell's equations show that E and B fields are related by this mathematical property.
What is symmetry (or duality)?
This wave phenomenon occurs when the electric field of an EM wave is confined to a specific orientation, such as the x-axis.
What is polarization?
This Maxwell Equation states that a time-varying magnetic field creates a circulating electric field, providing the mathematical basis for calculating induced electromotive force (EMF)
What is Faraday’s Law of Induction?
This dimensionless ratio compares the energy stored in an oscillator to the average power dissipated per cycle.
What is the Quality factor (or Q)?
In the complex impedance formula Z=R+iX, this is the specific name for the imaginary part X.
What is reactance?
He is the physicist who "fixed" Ampere's Law by adding a term for changing electric fields.
Who is James Clerk Maxwell?
This is the specific term for the time-averaged energy flux of a fixed-frequency EM wave.
What is irradiance (or intensity)?
These dual differential equations describe the behavior of current and voltage pulses traveling down a line by relating their spatial derivatives to their time derivatives via the line’s inductance and capacitance per unit length
(Not a law but close enough)
What are the Telegrapher’s Equations?