Capacitor charging and discharging
PARTS AND MATERIALS
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6 volt battery
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Two large electrolytic capacitors, 1000 �F
minimum (Radio Shack catalog # 272-1019, 272-1032, or
equivalent)
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Two 1 kΩ resistors
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One toggle switch, SPST ("Single-Pole,
Single-Throw")
Large-value capacitors are required for this
experiment to produce time constants slow enough to track
with a voltmeter and stopwatch. Be warned that most large
capacitors are of the "electrolytic" type, and they are
polarity sensitive! One terminal of each capacitor
should be marked with a definite polarity sign. Usually
capacitors of the size specified have a negative (-) marking
or series of negative markings pointing toward the negative
terminal. Very large capacitors are often polarity-labeled
by a positive (+) marking next to one terminal. Failure to
heed proper polarity will almost surely result in capacitor
failure, even with a source voltage as low as 6 volts. When
electrolytic capacitors fail, they typically explode,
spewing caustic chemicals and emitting foul odors. Please,
try to avoid this!
I recommend a household light switch for the
"SPST toggle switch" specified in the parts list.
CROSS-REFERENCES
Lessons In Electric Circuits, Volume
1, chapter 13: "Capacitors"
Lessons In Electric Circuits, Volume
1, chapter 16: "RC and L/R Time Constants"
LEARNING OBJECTIVES
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Capacitor charging action
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Capacitor discharging action
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Time constant calculation
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Series and parallel capacitance
SCHEMATIC DIAGRAM
ILLUSTRATION
INSTRUCTIONS
Build the "charging" circuit and measure
voltage across the capacitor when the switch is closed.
Notice how it increases slowly over time, rather than
suddenly as would be the case with a resistor. You can
"reset" the capacitor back to a voltage of zero by shorting
across its terminals with a piece of wire.
The "time constant" (τ) of a resistor
capacitor circuit is calculated by taking the circuit
resistance and multiplying it by the circuit capacitance.
For a 1 kΩ resistor and a 1000 �F capacitor, the time
constant should be 1 second. This is the amount of time it
takes for the capacitor voltage to increase approximately
63.2% from its present value to its final value: the voltage
of the battery.
It is educational to plot the voltage of a
charging capacitor over time on a sheet of graph paper, to
see how the inverse exponential curve develops. In order to
plot the action of this circuit, though, we must find a way
of slowing it down. A one-second time constant doesn't
provide much time to take voltmeter readings!
We can increase this circuit's time constant
two different ways: changing the total circuit resistance,
and/or changing the total circuit capacitance. Given a pair
of identical resistors and a pair of identical capacitors,
experiment with various series and parallel combinations to
obtain the slowest charging action. You should already know
by now how multiple resistors need to be connected to form a
greater total resistance, but what about capacitors? This
circuit will demonstrate to you how capacitance changes with
series and parallel capacitor connections. Just be sure that
you insert the capacitor(s) in the proper direction: with
the ends labeled negative (-) electrically "closest" to the
battery's negative terminal!
The discharging circuit provides the same
kind of changing capacitor voltage, except this time the
voltage jumps to full battery voltage when the switch closes
and slowly falls when the switch is opened. Experiment once
again with different combinations of resistors and
capacitors, making sure as always that the capacitor's
polarity is correct.
COMPUTER SIMULATION
Schematic with SPICE node numbers:
Netlist (make a text file containing the following text,
verbatim):
Capacitor charging circuit
v1 1 0 dc 6
r1 1 2 1k
c1 2 0 1000u ic=0
.tran 0.1 5 uic
.plot tran v(2,0)
.end
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