Charging Capacitors: Time-Dependent Current and Circuits Analysis

This lecture explores the process of charging capacitors using experiments with cylindrical capacitors and batteries, analyzing circuits with capacitors in parallel and series, and deriving differential equations to understand the time-dependent current. The instructor demonstrates how the energy stored in capacitors affects the circuit's behavior, introduces the concept of time constant tau as the product of resistance and capacitance, and explains the exponential charging and discharging behavior of capacitors. By examining the total capacitance in parallel and series circuits, students learn how to calculate the overall capacitance and understand the relationship between capacitors, resistors, and time constants.