Last Minute Lecture

Alternating Current, Circuits & Transformers Explained | Chapter 31 of University Physics In Chapter 31, we explore alternating current (AC) fundamentals, from sinusoidal sources and phasors to reactive circuit elements, resonance, and the operation of transformers—key to power distribution and modern electronics. Watch the full video summary here for in-depth walkthroughs and phasor demonstrations. Phasors & Sinusoidal Sources AC voltages and currents vary as v(t) = V max cos(ωt) , where ω = 2πf . Phasors represent these sinusoids as rotating vectors in the complex plane, simplifying circuit analysis: RMS values: V rms = V max /√2 , I rms = I max /√2 US AC frequency: 60 Hz (ω ≈ 377 rad/s); Europe: 50 Hz (ω ≈ 314 rad/s). Resistance & Reactance Resistor (R): V R = I R , voltage and current in phase. Inductor (L): V L = I X L , X L = ωL , voltage leads current by 90°. Capacitor (C): V C = I X C , X C = 1/(ωC) , voltage lags current by...

Sources of Magnetic Fields Explained | Chapter 28 of University Physics Chapter 28 explores how moving charges and currents create magnetic fields, and how materials respond to those fields. You’ll master the Biot–Savart Law for calculating field contributions, Ampère’s Law for symmetric configurations, and the role of magnetic susceptibility and permeability in different materials. Watch the full video summary for detailed derivations and visualizations. Magnetic Field from a Moving Charge A single charge moving with velocity v generates a magnetic field given by the equation: B = (μ₀/4π) · [q v × r̂ / r²] Here, μ₀ is the magnetic constant, q the charge, and r̂ the unit vector from the charge to the field point. The field lines form closed loops and obey the superposition principle. Biot–Savart Law & Applications The Biot–Savart Law extends this idea to current elements: dB = (μ₀/4π) · [I dl × r̂ / r²] By integrating over a wire, you find: Long straight wir...

Magnetic Fields & Forces – Moving Charges & Currents Explained | Chapter 27 of University Physics Chapter 27 dives into how moving charges and currents generate and respond to magnetic fields. From the fundamental Lorentz force to real-world applications like mass spectrometers and DC motors, you’ll build the foundation for electromagnetism. Watch the full video summary on YouTube for demonstrations of magnetic forces and device applications. Fundamentals of Magnetism Magnetic fields arise from moving electric charges. Every magnet has a north and south pole—no isolated monopoles exist. In practice, charges create the field, then other moving charges feel a force within it. The Magnetic Field (B) The magnetic field B is a vector field measured in tesla (T), with lines forming closed loops from north to south poles. Field line density indicates strength, and a compass aligns with the local field direction. Magnetic Force on a Moving Charge The Lorentz force law ...