Hands-on RC Circuits

NS543 Project

Don Rhine

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)

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)

,( ) ( )t

RCC S C initial SV t V V V e

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

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

Alg II and TEAMS Versions...• 6 Pre-fabbed charge-discharge circuits

• Select RC values in 3-10 second rangeS1

CLOSED

9V Battery

R1

+

C

R2

I

PUSH & HOLD

S1

9V Battery

R1

+

C

S2 CLOSED

R2

I

PUSH & HOLD

Hook RED probe here

Hook BLACK probe here

Diagram 3

Charging:

Discharging:

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

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

Excel Template

Excel Graph

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

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

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

For Your AP Calc Students...

• Kirchoff’s Voltage LawVS – 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?