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...

Sound Waves – Properties, Behavior & Applications Explained | Chapter 16 of University Physics Chapter 16 explores how sound waves propagate through different media and manifest in phenomena like resonance, interference, beats, and the Doppler effect. You’ll learn the basics of longitudinal mechanical waves, how we measure and perceive them, and their critical applications in acoustics and engineering. Watch the full video summary here for detailed explanations and demonstrations. What Is a Sound Wave? Longitudinal wave: particles oscillate parallel to wave propagation. Audible range: 20 Hz to 20 kHz (infrasonic below, ultrasonic above). Phase relation: pressure and displacement are 90° out of phase. Pressure wave model: p(x, t) = B k A sin(kx – ωt). Speed of Sound In fluids: v = √(B/ρ), where B is bulk modulus. In solids: v = √(Y/ρ), with Y Young’s modulus. In gases: v = √(γRT/M), rising with temperature. Wavelength relation: λ = v/f. ...

Periodic Motion & Simple Harmonic Oscillations Explained | Chapter 14 of University Physics Chapter 14 delves into periodic motion and simple harmonic motion (SHM), covering how restoring forces produce oscillations, the mathematical models for springs and pendulums, energy exchange in oscillators, and the effects of damping and driving forces. Watch the full video summary here for step-by-step derivations and examples. Describing Periodic Motion Periodic motion repeats in cycles, characterized by: Amplitude (A): Maximum displacement from equilibrium Period (T): Time for one complete cycle Frequency (f): Cycles per second (Hz), f = 1/T Angular frequency (ω): 2πf Simple Harmonic Motion SHM arises when a restoring force is proportional to displacement, as in Hooke’s Law: F = –k x The solutions for motion are sinusoidal: x(t) = A cos(ωt + φ) v(t) = –ω A sin(ωt + φ) a(t) = –ω² x(t) Where ω = √(k/m) , giving the period and frequency independe...