PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A circuit contains a battery of fixed emf, an ideal resistor R, an initially uncharged capacitor C, and an incandescent bulb whose filament resistance remains approximately constant during operation. Two ideal switches, S1 and S2, control the current pathways as described below:
• S1 lies in series with both the resistor–capacitor combination and the bulb.
• S2 is wired so that, when closed, it bypasses the resistor R but does not bypass the capacitor or the bulb.
At time t=0, both switches are open.
Answer the following qualitative questions about bulb brightness, assuming brightness is directly related to the instantaneous current through the bulb.
(a) S1 is closed at t=0 while S2 remains open. Describe how the brightness of the bulb changes from t=0 until a long time afterward. Explain your reasoning in terms of charge flow, potential differences, and the state of the capacitor.
(b) At a later time t=t1 (after the bulb has noticeably dimmed), switch S2 is closed while S1 remains closed. Predict the immediate effect on bulb brightness and explain why this change occurs.
(c) Sketch qualitatively a graph of bulb brightness versus time from t=0 to a time well after t=t1. Clearly label key features corresponding to the switch operations and describe those features in words.
(d) Suppose instead that S2 had been closed first and S1 closed second. Discuss which component—the resistor–capacitor branch or the bulb—would first carry current, and predict which bulb-brightness behavior would be observed immediately after the second switch is closed. Provide justification based on closed-loop requirements.