Category: Part 3: Electricity

Problem Statement Solve the capacitor/capacitance problem: Irodov Problem 3.22. Series: $1/C = 1/C_1+1/C_2+ $; Parallel: $C = C_1+C_2+ $. For $C_1=2$, $C_2=3$, $C_3=6\,\mu$F: series $C=1\,\mu$F, parallel $C=11\,\mu$F. Given Information Plate area $A$ (for parallel plate) or geometry as given Separation $d$ or radii as given Dielectric constant $\kappa$ (if applicable, else $\kappa=1$ for vacuum) Permittivity…

Problem Statement Irodov Problem 3.56. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key is to identify which conservation law or field equation governs the system, then apply it systematically. Dimensional…

Problem Statement Solve the capacitor/capacitance problem: Irodov Problem 3.23. $Q_0 = 800\,\mu$C split between $C_1=4\,\mu$F and $C_2=6\,\mu$F: $V_f = 80\,\text{V}$. Energy lost = $48\,\text{mJ}$ (dissipated in wire/spark). Given Information Plate area $A$ (for parallel plate) or geometry as given Separation $d$ or radii as given Dielectric constant $\kappa$ (if applicable, else $\kappa=1$ for vacuum) Permittivity…

Problem Statement Solve the capacitor/capacitance problem: Irodov Problem 3.19. $$U = \frac{Q^2}{2C} = \frac{1}{2}CV^2$$ Energy density: $u = \varepsilon_0 E^2/2$ (general result). Given Information Plate area $A$ (for parallel plate) or geometry as given Separation $d$ or radii as given Dielectric constant $\kappa$ (if applicable, else $\kappa=1$ for vacuum) Permittivity $\varepsilon_0 = 8.85\times10^{-12}\,\text{F m}^{-1}$ Physical…

Problem Statement Analyze the circuit: Irodov Problem 3.53. $R(T) = R_0[1+\alpha(T-T_0)]$. At 100°C: $R = 10(1+0.393) = \boxed{13.93\,\Omega}$. $R=15\,\Omega$ at $T=127°\text{C}$. Given Information Resistance values $R_1, R_2, \ldots$ as specified EMF $\mathcal{E}$ and internal resistance $r$ of battery Any additional circuit elements given Physical Concepts & Formulas Ohm’s Law $V = IR$ and Kirchhoff’s two…

Problem Statement Solve the capacitor/capacitance problem: Irodov Problem 3.20. $$\boxed{F = \frac{Q^2}{2\varepsilon_0 A} = \frac{\sigma^2 A}{2\varepsilon_0}}$$ Factor of $1/2$: each plate is in the field of the other plate only. Given Information Plate area $A$ (for parallel plate) or geometry as given Separation $d$ or radii as given Dielectric constant $\kappa$ (if applicable, else $\kappa=1$…

Problem Statement Analyze the circuit: Irodov Problem 3.54. KCL: $\sum I_{\text{in}} = \sum I_{\text{out}}$ (charge conservation). $I_3 = I_1+I_2 = 4+1.5 = \boxed{5.5\,\text{A}}$. Given Information Resistance values $R_1, R_2, \ldots$ as specified EMF $\mathcal{E}$ and internal resistance $r$ of battery Any additional circuit elements given Physical Concepts & Formulas Ohm’s Law $V = IR$ and…

Problem Statement Solve the capacitor/capacitance problem: Irodov Problem 3.17. $$\boxed{C = 4\pi\varepsilon_0\frac{ab}{b-a}}$$ As $b\to\infty$: isolated sphere $C = 4\pi\varepsilon_0 a$. Given Information Plate area $A$ (for parallel plate) or geometry as given Separation $d$ or radii as given Dielectric constant $\kappa$ (if applicable, else $\kappa=1$ for vacuum) Permittivity $\varepsilon_0 = 8.85\times10^{-12}\,\text{F m}^{-1}$ Physical Concepts &…

Problem Statement Analyze the circuit: Irodov Problem 3.51. Differential: $\mathbf{j} = \sigma\mathbf{E}$. Field in wire: $E = \rho j = 1.7\times10^{-8}\times10^6 = \boxed{17\,\text{mV/m}}$. Given Information Resistance values $R_1, R_2, \ldots$ as specified EMF $\mathcal{E}$ and internal resistance $r$ of battery Any additional circuit elements given Physical Concepts & Formulas Ohm’s Law $V = IR$ and…

Problem Statement Solve the capacitor/capacitance problem: Irodov Problem 3.18. $$\boxed{C = \frac{2\pi\varepsilon_0 l}{\ln(b/a)}}$$ Per unit length: $C/l = 2\pi\varepsilon_0/\ln(b/a)$. Given Information Plate area $A$ (for parallel plate) or geometry as given Separation $d$ or radii as given Dielectric constant $\kappa$ (if applicable, else $\kappa=1$ for vacuum) Permittivity $\varepsilon_0 = 8.85\times10^{-12}\,\text{F m}^{-1}$ Physical Concepts & Formulas…