1. Hands-on RC Circuits NS543 Project Don Rhine

2. Audience & Timing • Honors Physics students (11-12 grade) • After exploring introductory capacitor equations • After resistive circuit analysis • 4 periods • Honors Algebra II students (10-11 grade) • At end of unit on exponential & logarithmic functions • 1½ periods (~ 52 minute period)

3. Physics Learning Objectives • Practice real calculations involving capacitors and resistors • Practice with Units, SI Prefixes, and Scientific Notation • Expose students to actual component and building circuits • Develop better qualitative understanding of behavior of capacitors in DC circuits • Develop qualitative understanding and experimentally verify model given by textbook: • Use TI-8x and Excel for calculations, data collection, analysis • Use advanced knowledge from Algebra II/PreCalc in Physics! • For students in AP Calc, practical application of 1st order Differential Equations (derive relationship)

4. Math Learning Objectives • Answer nagging questions: • When will I ever use this? • What is this used for? • Practical hands-on demonstration: • exponential growth & decay functions – happens in real-time, right in front of their eyes • the natural base, e • using logarithms to solve for variables in exponents (inverse functions) • Using TI-8x to collect, share, and analyze data

5. History • Originally developed for Algebra II (2004?) hands-on activity at end on exponential growth & decay and logarithms unit • Extended to advanced application for TEAMS Academy students (“AP” level) (2007 – 2009) • Introduced unknown C and R2 • Students had to develop method to find unknowns • Use math skills above and function transformations & translations, differential equations • Introduce concept of physics/math prediction/modeling and comparing to experimental results • Reworked this year for Honors Physics

6. I Alg II and TEAMS Versions... • 6 Pre-fabbed charge-discharge circuits • Select RC values in 3-10 second range R1 S1 CLOSED PUSH & HOLD Charging: I C + 9V Battery R2  R1 S1 S2 CLOSED PUSH & HOLD Discharging: C + Hook RED probe here 9V Battery R2  Hook BLACK probe here Diagram 3

7. Alg II and TEAMS Versions...Project on-screen as data is collected on TI-8x, then share data

8. Pre-Lab ExerciseBefore & After: R vs. RC Circuit • Before: • Define “current” (review) • Close SW. I = ? • Capacitor Calcs • Given V and C, Q = ? • Given I above, how long to “fill” C? • After: Add C - Qualitative • C appears to be “open circuit” • What happens just after SWA closed? • What happens a long time later? • Use formula and compare results • Meaning and units of RC? • Create table of values/excel BEFORE AFTER

9. Excel Template

10. Excel Graph

11. Final Result for Pre-Lab ExerciseThis graphic posted on front of wiki week before lab!

12. Lab ExerciseDoes it really work?? • Preliminary Calcs (HW): • More practice with calcs. and qualitative results • Practice Alg skills – solve for t, R, C • Use of table for 1, 2, 3, etc. • Lab: • Calculate & choose R & C values from stock • Build circuit • Test & collect 200 data points • Export to Excel for analysis and modeling exercise

13. Conclusion • RC circuit is nice demo for Algebra II, and can be adapted for advanced students • Simulations are nice (if you can find a good one)...but seeing is believing • Inexpensive hands-on lab allows students to practice a variety of skills • Connecting skills & terminology learned in math class to a practical application • Applications of RC circuits

14. For Your AP Calc Students... • Kirchoff’s Voltage Law VS – VR – VC = 0 VS – I*R – q/C= 0 VS – (dq/dt)*R – q/C= 0 If VS, R, C are constant, solve for q?