A charged capacitor of capacitance is connected across a resistor of resistance at time
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A charged capacitor of capacitance C is connected across a resistor of resistance R at time t=0, allowing it to discharge. After a time t=2.0ms the resistor is instantaneously replaced by a different resistor of resistance 3R, and the discharge continues.
Assume all connections are ideal and ignore any inductive effects.
(a) On clearly labeled axes, sketch the qualitative shape of the current-versus-time graph from t=0 until a time long after the substitution. Indicate on the time axis the instant t=2.0ms and mark at least one point associated with a characteristic time constant before and after the substitution.
(b) Explain how the substitution affects the instantaneous current just after t=2.0ms. Justify your answer without performing explicit calculations.
(c) Compare the total amount of charge that leaves the capacitor during the first 2.0ms with the total amount of charge that leaves during the next 4.0ms after the substitution. Provide qualitative reasoning that refers to the time constants involved.
(d) Suppose instead that, at t=2.0ms, the original resistor R were replaced by a resistor of resistance 31R. Discuss how each of your answers in parts (a) through (c) would change, if at all, and explain the physical basis for any differences.