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
The equation follows by applying the physical law to the chosen system; ideal constraints link the variables. Signs must remain consistent with the defined directions.
problems.proof.pitfall. Pitfall: do not change sign conventions between equations; a negative sign may encode direction rather than an invalid result.