A capacitor is allowed to charge through a resistor from an ideal dc supply
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A capacitor is allowed to charge through a resistor R1 from an ideal dc supply. After the capacitor voltage reaches exactly one-half of its eventual steady-state value, the experimenter instantaneously replaces R1 with a different resistor R2 and allows the circuit to continue charging toward the same supply voltage.
(a) At the moment immediately after R2 is substituted, describe qualitatively how the current in the circuit compares with the current that existed just before the substitution. Explain your reasoning in terms of circuit quantities that remain unchanged and those that change abruptly.
(b) On separate, clearly labeled qualitative axes, sketch the expected shapes of the capacitor-voltage curve and the current-versus-time curve for the entire experiment, beginning at t=0 (when charging starts) and ending at a time long after the substitution. Indicate the instant at which the resistor is changed and label key features such as slopes and asymptotes.
(c) Explain how the slopes of the capacitor-voltage curve just before and just after the substitution are related to R1 and R2, respectively. Describe what measurable aspect of your sketch conveys this information.
(d) Suppose R2=31R1. Without using the explicit exponential form of the charging equation, determine whether the time required for the capacitor to charge from one-half to three-quarters of its final voltage after the substitution is greater than, less than, or equal to the time required for the initial rise from zero to one-quarter of its final voltage. Justify your answer qualitatively.