PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
During a practical assessment, a student is asked to sketch the current through a resistor immediately after an uncharged capacitor in series with that resistor is connected across an ideal battery. The student’s sketch is reproduced below in text form:
• The current starts at a non-zero value at t=0.
• The curve decreases linearly to zero at t=τ.
• The current remains exactly zero for t>τ.
Assume the resistor and capacitor remain unchanged throughout the experiment.
(a) Critique the student’s sketch by identifying each feature that is inconsistent with the expected physical behavior of the circuit.
(b) For each inconsistency you identified, explain the underlying physical principle that the student failed to consider.
(c) Redraw—again in words or using a qualitative sketch—the current-versus-time graph that correctly represents the behavior of the circuit from t=0 to t≫τ. Clearly describe how your corrected graph differs from the student’s original and justify each difference in terms of circuit physics.
(d) The student claims that the current must reach zero exactly at t=τ because that is "the definition of the time constant." Construct a concise argument, grounded in the definition of time constant, that addresses this misconception.