Problem 2
An ideal capacitor of capacitance C is charged to voltage V₀ and connected at t=0 to a resistor R initially carrying no current. Define discharge current as positive in the discharge direction and v(t) with the initial capacitor polarity; neglect inductance and wire resistance. (a) Establish the discharge differential equation and time constant τ. (b) Find v(t) and current i(t) for t≥0. (c) Calculate heat dissipated from 0 to t and check its limit as t approaches infinity. Use SI units throughout and treat components as ideal exactly as specified. State sign conventions when writing equations and retain units in final results.
problems.proof.stepOf
problems.proof.analysis
First identify the system, given quantities, and sign convention; this determines what is conserved or acts on the body. The stated idealizations exclude unmentioned forces or effects.