PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A circuit consists of an ideal battery of emf E, a resistor of resistance R, a capacitor of capacitance C, an ideal switch S, and connecting wires of negligible resistance. At time t=0 the capacitor is uncharged and the switch is closed, allowing the capacitor to charge through the resistor.
Answer the following qualitatively. Numerical calculations are not required.
(a) Describe what happens to the magnitude of the current in the circuit between the instant just after S is closed and a time long after the closure. In your description, identify the current at t=0, at a time equal to one time constant, and as t→∞. Explain your reasoning.
(b) Describe how the potential difference across the capacitor evolves over the same time interval. In particular, state the approximate fraction of the final potential difference that exists across the capacitor after one time constant has elapsed, and explain why that fraction occurs.
(c) Sketch on separate, clearly-labeled axes the qualitative shapes of the graphs of (i) current versus time and (ii) capacitor voltage versus time for the charging process. On each graph, mark the point corresponding to one time constant and label its numerical value on the vertical axis as a fraction or multiple of the initial or final value.
(d) Suppose the resistance is instantly doubled while the capacitor is still charging. Without further calculation, explain how, if at all, each of the following changes compared with the original situation: the slope of the current-versus-time graph at the instant of the change, the new time constant, and the time it now takes for the capacitor to reach 90 % of its final voltage.