Electromagnetism & Electricity

Explore parameters of magnetic circuits, including flux, magnetomotive force, reluctance, permeability, and flux density B and magnetic field intensity H, and their relationships in closed magnetic paths.

Learn to calculate reluctance and flux in basic magnetic circuits by determining path length and cross-section area, using μ0, relative permeability, and MMF from current and turns.

Explore series and parallel magnetic circuits, relate reluctance and mmf to flux, and apply Ohm's law analogies to iron and alloy materials with varying length and cross-section.

Explore two examples of a series–parallel magnetic circuit, calculate total reluctance and flux, and determine the current needed to achieve target flux in iron and air-gap paths.

Compare magnetic and electric circuits by mapping magnetic flux to current and reluctance to resistance, highlighting similarities in definitions and equations while noting differences in flux behavior and energy.

Explore the magnetization curve and core saturation, showing how flux density and field intensity deviate from linearity as permeability varies, and how knee point guides design.

Explore the hysteresis loop of a magnetic material as current climbs to saturation and returns, revealing residual flux, coercive force, and the difference between hard and soft materials.

Move a magnet or coil to change the magnetic flux linkage and induce an emf that powers a bulb, illustrating Faraday's law and electromagnetic induction.

Explore how moving magnets convert mechanical energy into electrical energy, driving current in a closed circuit and lighting a bulb through the rate of change of magnetic flux.

Understand how Lenz's law states induced emf opposes the change in magnetic flux. See how a moving magnet induces current in a coil, converting mechanical energy to electricity.

Explore statically induced emf from changing current in a coil, including self-induced emf, inductance, and how core material and reluctance affect flux.

Derive the expression of self-inductance by linking emf to the rate of change of current, showing emf is proportional to di/dt with a negative sign.

Derive the energy stored in an inductor by integrating power over time, yielding E = 1/2 L I^2 as current rises from 0 to I.

Explains how an inductor behaves: in steady state it acts as a short circuit, but during switching it produces high emf; flyback diode provides a freewheeling path to prevent sparks.

See how a dc circuit with an inductor starts at zero current and charges exponentially, with self-induced emf diminishing as the current approaches its steady maximum.

Derive exponential rise of current in a resistor-inductor circuit after a dc switch-on, define time constant lambda equals inductance over resistance, and show i(t) reaches 63.2% at t equals lambda.

Switching on an inductive circuit makes current rise exponentially while the inductor voltage decays. At t = λ, current reaches ~0.632 of max and voltage ~0.368 of supply.

Explains decay of current in an inductive circuit after switch-off, using a flyback diode for freewheeling, and derives I = Imax e^{-t/τ} with a 36.8% decay per time constant.

Analyze the rise and decay of current in a DC RL circuit, using the time constant lambda = L/R to solve charging and discharging examples with Imax and steady-state current.

Explore how changing current in one coil induces emf in a nearby coil through mutual induction, define mutual inductance M, mutual conductance, and coupling k with self-inductances L1 and L2.

Explore series and parallel inductors with and without mutual coupling, using dot notation to determine additive or subtractive flux. Derive the equivalent inductance formulas for series (L1+L2±2M) and parallel ((L1L2−M^2)/(L1+L2−2M)).

Analyze hysteresis losses in electromagnets, including core iron losses and i^2 r losses, with AC cycling generating heat; relate energy loss to the B-H loop area, frequency, and Steinmetz's law.

Explore how changing magnetic flux induces eddy currents in conductors, causing core losses, and how laminating iron cores with insulating layers reduces these losses in AC machines.

Explore the molecular theory of magnetism, including electron orbit and spin, alignment of tiny magnets under magnetic fields, and temperature effects that drive saturation and loss of magnetism.

explain how a current-carrying conductor in a magnetic field experiences a force that drives a coil rotor, producing torque and rotation, with a commutator reversing current for continuous motion.

A moving conductor in a magnetic field induces emf. Perpendicular motion yields emf = B L v; at any angle emf = B L v sin theta, max at 90.

Move a conductor through a magnetic field to induce an emf and current that opposes the motion, using Lenz's law and flux direction to determine clockwise or inward flow.

Explore how a coil rotating in a magnetic field generates emf, with current directions in its conductors, series and parallel connections, and how constant angular speed yields a sinusoidal emf.

explain how the frequency of induced ac depends on rotor speed and pole count, noting two-pole machines yield cycle per 360-degree turn and four-pole machines yield cycle per 180-degree turn.

Explore practical generator designs with stationary magnets and rotating fields, using electromagnets to control voltage and reduce slip rings. Understand self-excited alternators and multi-pole configurations for efficiency.