Problem 2

A series circuit has resistance

R

and ideal capacitance

C

, initially uncharged, connected at

t=0

to a constant battery

V

. Find the charge as a function of time. Assume ideal objects and components, neglect unstated losses, and use SI units. (a) Derive the primary requested quantity from the appropriate law. (b) Analyze quantitatively how the result depends on the given parameters. (c) Check a physically meaningful limiting case and explain its meaning. State sign conventions, show reasoning, and check dimensions. (a) Calculate the requested quantity from the data. (b) Give the law or expression showing parameter dependence. (c) Examine a limit consistent with the model.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

i(t)=\frac VR e^{-t/(RC)}

problems.proof.analysis

Substituting the result into the requested relation shows how parameters affect the answer instead of treating the parts as unrelated.