Final answer:
The question involves using Laplace transforms to determine time-dependent expressions in an electrical circuit. Laplace methods are more accurate than graphical methods for this type of analysis. The question is from the field of Physics, specifically electromagnetic theory and circuit analysis.
Step-by-step explanation:
The question relates to the time-dependence of physical quantities described by equations, specifically in the context of electrical circuits involving a capacitor. When considering the approach to find and plot v_c(t), the correct choice is: b) Laplace methods. This is because Laplace transforms are particularly useful in solving differential equations that arise in the analysis of circuits and can directly provide expressions for the time-varying quantities such as voltage across a capacitor (V(t)) and the rate of change of voltage (dv(t)/dt).
The subject of this question is Physics, specifically related to electromagnetism and circuit analysis. If we were to analyze a circuit over time, using the Laplace transform allows us to turn differential equations into algebraic ones which are simpler to solve. After obtaining the solution in the s-domain, we can transform it back to the time domain to get the required time-dependent expressions like E(t), B(t), and the magnitude of the Poynting vector (S).
Regarding the comparison between graphically solving a problem and using analytical methods, analytical techniques are generally more accurate because they are not subject to the interpretation errors of graphing and provide exact mathematical expressions rather than estimates.