Data Sheet

-80-
142. The Number e
Build the circuit shown on the left and turn on the switch (62). Place
the magnet (7) near the reed switch (83) and you will see the heart LED
(69) light. Move the magnet (7) away from the reed switch (83) and
the heart LED (69) will stay bright for a little while and then turn dim.
As discussed in project #133, the voltage of the capacitor decays with
a time constant of R*C. The decay rate is given by e
-t/(R*C)
where e is a
constant known as Euler’s number, named after Swiss mathematician
Leonhard Euler, and t represents time in seconds. The value of e is
approximately 2.71828.
143. Time Constant t
Replace the 1kW resistor (42) in project #142 with the 5.1kW resistor
(43) and turn on the switch (62). Place the magnet (7) near the reed
switch (83) and you will see the heart LED (69) light. Move the magnet
(7) away from the reed switch (83) and the heart LED (69) will stay
bright for a while and then turn dim. As discussed in project #133,
the time constant for an RC circuit is R*C and is often times given the
symbol t. Note from the previous project that when time t = t = R*C,
then the signal has decayed by e
-1
= 0.367 or by approximately 37%
below its maximum value.
144. t for 10kW Resistor and 470mF Capacitor
Replace the 1kW resistor (42) in project #142 with the 10kW resistor
(44) and then turn on the switch (62). Place the magnet (7) near the
reed switch (83) and you will see the heart LED (69) light. Move the
magnet (7) away from the reed switch (83) and the heart LED (69) will
stay bright for a several seconds and then turn dim. The t for this circuit
is 10,000*470e
-6
= 4.7 seconds.
145. t for 100kW Resistor and 470mF Capacitor
Replace the 1kW resistor (42) in project #142 with the 100kW resistor
(45) and then turn on the switch (62). Place the magnet (7) near the
reed switch (83) and you will see the heart LED (69) light. Move the
magnet (7) away from the reed switch (83) and the heart LED (69) will
stay bright for a long time and then turn dim. The t for this circuit is
100,000*470e
-6
= 47 seconds.
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