An RC circuit contains an initially uncharged capacitor of capacitance connected in…
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Electric Circuits · Electric Circuits
Problem
An RC circuit contains an initially uncharged capacitor of capacitance C connected in series with a variable resistor and an ideal battery of emf E. At t=0 the switch is closed and the resistor has value R1. At a later time t=t1 (where t1 is comparable to the initial time constant) the resistance is suddenly changed to a new value R2 while the circuit continues to operate.
Answer the following qualitatively, supporting each response with clear reasoning.
(a) On a single set of axes, sketch the qualitative shape of the current-versus-time graph from t=0 to a time several time constants after t1. Clearly label the following on your sketch: the instant t=0, the instant t=t1, the initial slope, and the approximate slopes just before and just after t=t1.
(b) Explain how the magnitude of the time constant changes at t=t1 and describe its effect on the subsequent curvature of the current-versus-time graph.
(c) Suppose R2<R1. Compare the charge on the capacitor just after t=t1 with the charge it would have had at the same instant if the resistance had never been changed from R1. Provide a qualitative explanation based on the behavior of current before the change.
(d) Discuss how your answers to parts (a) through (c) would differ, if at all, if R2 were instead greater than R1. Emphasize the physical reasoning rather than repeating the sketches.