RC Circuits Explained: Exponential Growth and Decay

This lecture explores the mathematics of exponential growth and decay, starting with a frog population model before diving into RC circuits. Using Kirchhoff’s voltage rule, I derive the differential equations governing charge and current for two key cases: a discharging capacitor and a charging capacitor connected to an EMF source. Remarkably, the solutions mirror our earlier discussion of exponential change. Special attention is given to the RC time constant, revealing its physical significance in determining charge and discharge rates. Finally, I apply real-world values to solve for the initial current, final charge, and the time required to reach 99% of full capacity. This is a must-watch for mastering the physics and math behind RC circuits!
(NEW) Study guide with screenshots for this lecture is here:
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Problem set for this lecture is here:
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