PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Electric Circuits · Electric Circuits
Problem
Three RC circuits, each connected to an identical ideal DC power supply, are described below.
• Circuit P: One resistor of resistance R0 is in series with one capacitor of capacitance C0.
• Circuit Q: Two identical resistors, each of resistance R0, are connected in series; that series combination is placed in series with a single capacitor of capacitance C0.
• Circuit R: Two identical capacitors, each of capacitance C0, are connected in series; that series combination is placed in series with a single resistor of resistance R0.
All capacitors begin uncharged at the instant the circuits are completed.
Answer the following questions about the relative charging behavior of the three circuits.
(a) Identify which circuit will reach approximately 63 percent of its final charge in the shortest time. Provide a qualitative explanation that references the effective resistance and capacitance of the circuit without performing numeric calculations.
(b) Rank the three time constants τP,τQ,and τR from smallest to largest. Support your ranking with clear reasoning based on series-parallel combinations of the components.
(c) A second capacitor of capacitance C0 is connected in parallel with the existing capacitor in Circuit P, creating a new Circuit P′. Predict qualitatively how the time constant of Circuit P′ compares with those of Circuit P and Circuit R, and justify your prediction.