PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A circuit consists of an ideal 12 V battery, a 200 Ω resistor, and a 50 μF capacitor connected in series. At time t = 0, a switch is closed, connecting the three elements in a single loop. The capacitor is initially uncharged.
(1) Determine the current in the circuit immediately after the switch is closed.
(2) Applying energy conservation to a differential element of charge moving around the loop, derive an expression for the current I(t) as a function of time during the charging process.
(3) Calculate the time required for the potential difference across the capacitor to reach 9.0 V.
(4) After a very long time, the current in the circuit becomes negligible. Compute (i) the total energy delivered by the battery, (ii) the energy stored in the fully charged capacitor, and (iii) the energy dissipated as thermal energy in the resistor. Explain how your results are consistent with energy conservation.