PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
Three separate circuits—Circuit A, Circuit B, and Circuit C—each contain an identical ideal battery of emf E and an initially uncharged capacitor, but each uses a different resistor–capacitor combination as shown in the table below.
Circuit
Resistance
Capacitance
A
2R0
C0
B
R0
2C0
C
3R0
32C0
At time t=0 the switch in each circuit is closed so that the capacitors begin to charge.
(a) Determine which circuit’s capacitor reaches one-half of its final potential difference in the least amount of time. Justify your answer with appropriate reasoning and clearly show any symbolic comparisons you make among the circuits.
(b) Rank the three circuits in order of the time required for the current in each circuit to decrease to one-third of its initial value, from least time to greatest time. Explain your reasoning.
(c) Circuit B is modified by replacing its capacitor with two identical capacitors each of capacitance C0 that are connected (i) in series and separately (ii) in parallel. For each configuration, state whether the new time required to reach one-half of the final potential difference is less than, equal to, or greater than the original time in Circuit B, and justify your answer.