Physics Challenge for
Teachers and Students
Boris Korsunsky, Column Editor
Weston High School, Weston, MA 02493
korsunbo@post.harvard.edu
Solution to May 2015 Challenge
w A trip aCRoss the Bridge
Two identical capacitors, initially uncharged, are connected
to three identical resistors and an ideal voltage source in a
circuit shown below. The switch is closed at t = 0. Determine
the time t > 0 at which the current through the central resistor becomes zero. The values of R and C are given.
Kirchhoff ’s current law is applied to nodes A and B.
IC1 = IR2 + IB (4)
IC2 = IR1 + IB(5)
where
C
R
C
and
C2
R
R
C
(contributed by Matthew W. Milligan, Farragut High School,
Knoxville, TN)
Answer:
The branch currents IC1, IC2, IR1, IR2, and IB are assigned
in the direction as shown in figure.
(6)
(7)
Applying derivatives to Eqs. (1) and (2) and using (6) and
(7) identities, we have
I
I
.
(8)
(9)
Equations (4) and (5), and Eqs. (8) and (9) can be added
together:
Combining them, we have:
Kirchhoff ’s voltage law applied to the loops gives the following equations.
1
(1)
(2)
(3)
The Physics Teacher ◆ Vol. 53, 2015
From Eq. (3)
Combining the last two equations, we obtain a differential
equation for IB:
Therefore,
Discharged capacitors behave as short circuits when the
switch is closed at t = 0, and the circuit is equivalent to
three parallel resistors with current
Then
which is zero for
Thorsten Poeschel (University Erlangen-Nuremberg, Erlangen, Germany)
Joseph Rizcallah (School of Education, Lebanese
University, Beirut, Lebanon)
Rober Siddon (U. S. Naval Academy, Annapolis,
MD)
Jason L. Smith (Richland Community College, Decatur, IL)
Clint Sprott (University of Wisconsin – Madison,
WI)
Fred Tomblin (California Lutheran University,
Thousand Oaks, CA)
Guidelines for contributors:
(Submitted by Eduardo A. Heredia, Universidad de Buenos Aires, Buenos Aires, Argentina)
We also recognize the following successful contributors:
Utsav Banerjee (Kolkata, India)
Salvatore Basile (Università degli Studi di Palermo,
Palermo, Italy)
Phil Cahill (The SI Organization, Inc., Rosemont, PA)
Don Easton (Lacombe, Alberta, Canada)
John F. Goehl, Jr. (Barry University, Miami Shores, FL)
Supriyo Ghosh (Kolkata, India)
Gerald E. Hite (TAMUG, Galveston, TX)
Art Hovey (Galvanized Jazz Band, Milford, CT)
José Ignacio Íñiguez de la Torre (Universidad de
Salamanca, Salamanca, Spain)
Daniel Mixson (Naval Academy Preparatory School,
Newport, RI)
Carl E. Mungan (U. S. Naval Academy, Annapolis,
MD)
Paul Nahin (The University of New Hampshire,
Durham, NH)
Bill Nettles (Union University, Jackson, TN)
– We ask that all solutions, preferably in Word format, be submitted to the dedicated email address
challenges@aapt.org. Each message will receive
an automatic acknowledgment.
– The subject line of each message should be the
same as the name of the solution file.
– The deadline for submitting the solutions is the
last day of the corresponding month.
– Each month, a representative selection of the
successful solvers’ names will be published in
print and on the web. – If your name is—for instance—Brian May, please
name the file “May15May” (do not include your
first initial) when submitting the solution.
– If you have a message for the Column Editor, you
may contact him at korsunbo@post.harvard.
edu; however, please do not send your solutions
to this address.
Many thanks to all contributors; we hope to hear
from many more of you in the fall. We also hope to
see more submissions of the original problems –
thank you in advance!
Have a great summer!
Boris Korsunsky, Column Editor
The Physics Teacher
◆ Vol. 53, 2015