1. Exponential Function in Circuits, Part 1
K. A. Connor
Mobile Studio Project
Center for Mobile Hands-On STEM
SMART LIGHTING Engineering Research Center
ECSE Department
Rensselaer Polytechnic Institute
Intro to ECSE Analysis

2. The Exponential Function
Where found in nature?
Damped dynamic systems
Circuits
Properties of
It is its own derivative!
Series expansions
Small argument expressions
Characteristic distances and times

3. Damped Systems Friction Resistance Surface – dry, fluid, lubricated
Skin (flows around surfaces)
Internal
Static vs Kinetic
Resistance
Thermal
Electrical

4. Exponential Function
What does it look like?
Growing
Decaying

5. Deriviatives What is a derivative of a function? Examples

6. Exponential Function Series Representation Derivative More Generally
Proof:
More Generally

7. Exponential Functions
Small Argument Expression
Characteristic Distance and Times
d is distance function decays to

8. Exponential Function Characteristic Time For RC circuit τ = RC
For RL circuit τ = L/R
Why Different?

9. Exponential Function
Question – If the exponential function decays for all time or all distances, does the quantity it represents really never go to zero?