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:
•
VC (t )  VS  (VC ,initial  VS )e

t
RC
• 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)
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 range
R1
PUSH & HOLD
S1
CLOSED
Charging:
9V
Battery
I C
+

R2
R1
S2
CLOSED
S1
Discharging:
9V
Battery
+
C

I
PUSH & HOLD
Hook RED probe here
R2
Hook BLACK probe here
Diagram 3
Alg II and TEAMS Versions...
Project on-screen as data is collected on TI-8x, then share data
Pre-Lab Exercise
Before & 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?
BEFORE
• 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
AFTER
Excel Template
Excel Graph
Final Result for Pre-Lab Exercise
This graphic posted on front of wiki week before lab!
Lab Exercise
Does 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 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?