An Uncharged 30

question 24

Essay

An uncharged 30.0-µF capacitor is connected in series with a 25.0-Ω resistor,a DC battery,and an open switch.The battery has an internal resistance of 10.0 Ω and the open-circuit voltage across its terminals is 50.0 V.The leads have no appreciable resistance.At time t = 0,the switch is suddenly closed.
(a)What is the maximum current through the 25.0-Ω resistor and when does it occur (immediately after closing the switch or after the switch has been closed for a long time)?
(b)What is the maximum charge that the capacitor receives?
(c)When the current in the circuit is 0.850 A,how much charge is on the plates of the capacitor?

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Definitions:

Cognitive Shortcuts

Mental strategies or heuristics that simplify decision making by reducing the amount of processing required to come to conclusions.

Heuristics

Mental shortcuts or "rules of thumb" that simplify decision-making processes, often used unconsciously.

System I

A term from cognitive science referring to the fast, automatic, and often unconscious way of thinking, contrasted with slower, more deliberate thought.

Dual-Process Theory

The proposal that judgment involves two types of thinking: a fast, efficient, but sometimes faulty set of strategies, and a slower, more laborious, but less risky set of strategies.