Last Minute Lecture

Capacitance, Energy Storage & Dielectrics Explained | Chapter 24 of University Physics Chapter 24 explores how capacitors store electrical energy, how their arrangement in circuits affects overall capacitance, and how inserting dielectric materials enhances their performance. Dive into the definitions, formulas, and physical insights that make capacitors indispensable in electronics. Watch the full video summary on YouTube for detailed walkthroughs and examples. What Is Capacitance? A capacitor consists of two conductors separated by an insulator. When charged, one plate holds +Q, the other –Q. The capacitance C measures how much charge the device stores per unit voltage: C = Q / V , with units of farads (1 F = 1 C/V). For a parallel-plate capacitor: C = ε₀ A / d , where A is plate area and d the separation. Capacitors in Series and Parallel Capacitors combine differently than resistors: Series: same charge Q on each; total voltage adds. 1/C_eq = 1...

Electric Potential & Energy in Electric Fields Explained | Chapter 23 of University Physics Chapter 23 introduces electric potential—a scalar, energy-based perspective on electrostatics that often simplifies calculations compared to vector force approaches. You’ll learn about electric potential energy, voltage (potential difference), equipotential surfaces, and how electric fields relate to potential through gradients and line integrals. Watch the full video summary here for detailed derivations and examples. Electric Potential Energy (U) Electric potential energy ( U ) is stored due to charge configurations. The work done by the field equals the negative change in U: U = (1 / 4πε₀) · (q · q₀) / r for two point charges, with U defined as zero at r → ∞. For multiple charges, sum over unique pairs: U_total = Σ (1 / 4πε₀) · (q_i · q_j) / r_ij . Electric Potential (V) Electric potential ( V ) is the potential energy per unit test charge: V = U / q₀ , thus in volts (J/C...

Electric Flux & Gauss’s Law Explained | Chapter 22 of University Physics Electric flux and Gauss’s Law provide a powerful framework for calculating electric fields in systems exhibiting symmetry. In this chapter summary, we explore how flux through a surface relates to enclosed charge, apply Gauss’s Law to key geometries, and examine electrostatic behavior in conductors. Watch the full video summary here to see step-by-step derivations and visualizations of Gaussian surfaces. Electric Flux Electric flux ( Φ E ) measures the “flow” of electric field through a surface. For a flat surface of area A in a uniform field: Φ E = E · A · cos(φ) or Φ E = E ⋅ A . In general, for a curved or nonuniform field, flux is: Φ E = ∮ E ⋅ dA , where positive flux indicates field lines exiting the surface and negative flux indicates entry. Gauss’s Law Gauss’s Law links electric flux through a closed surface to the net charge enclosed: ∮ E ⋅ dA = Q enclosed / ε 0 . This law is equ...

Electric Charge & Electric Fields Explained | Chapter 21 of University Physics Chapter 21 lays the groundwork for understanding electrostatics by exploring how objects acquire charge, how charged particles interact via Coulomb’s law, and how the electric field concept unifies these interactions. This chapter also shows how to visualize fields with field lines and calculate fields for both point charges and continuous charge distributions. Watch the full video summary on YouTube for step-by-step examples and field visualizations. Electric Charge & Conservation Electric charge comes in two types—positive and negative—with like charges repelling and opposites attracting. Protons carry positive charge, electrons negative, and neutrons are neutral. The conservation of charge principle states that the total charge in a closed system remains constant, meaning charge can be transferred but never created or destroyed. Charging by Friction, Polarization & Induction Obj...