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 next part uses the preceding result as input rather than treating parts independently. This keeps conventions and physical state consistent throughout.
problems.proof.pitfall. Pitfall: do not change sign conventions between equations; a negative sign may encode direction rather than an invalid result.